Why do you need a Next key for LetterWise?
Wouldn't it be better just to hit the same key again if the letter you want doesn't appear first?

It seems this question arises mainly from some combination of the following beliefs:

That LetterWise is really just like Multi-tap.
That users are used to using just one key to produce a letter.
That a separate Next key makes the LetterWise interface more complex, difficult to use, slower, etc.

All of these are false.

Many factors argue for the use of a separate Next key in LetterWise

1) No timeout / simpler UI.
2) Smoother, faster text entry.
3) Simplifying the user interface.
4) Making error correction simpler.
5) A smaller, simpler product.
6) Put the infrequent action on a separate key.
7) Product testing.
8) LetterWise is not multi-tap.

These points are explained below.

1) No timeout / simpler

Many words contain consecutive letters that appear on the same key of a 12-key keyboard. For example, in the word "no", both letters appear on the 6 key.

To enter such a pair in a multi-tap system, it must be made clear which taps on the key apply to the first intended letter and which to the second. To enter "no" using multi-tap, 5 taps on the 6 key are required (2 for the n, 3 for the o). Between the 2nd and 3rd taps on the 6 key, something has to happen to specify the transition from the first letter to the next.

A very common solution is to let the system decide when a transition has happened by means of a timeout period. If the user pauses for longer than the timeout period, the system considers that subsequent keystrokes will be used to produce an additional letter. Thus to enter "no", a user would type 6 6 (wait) 6 6 6.

Unfortunately, the timeout approach creates more problems than it solves:

There is a single timeout period, whereas there are many users and individual users change their speed with context and familiarity. Thus a one-size-fits-all timeout period can be expected to be either too long or too short for almost all users.

A timeout that is too short leads to errors and therefore error correction. If when typing a "c", the timeout period expires between the 2nd and 3rd taps, the user will see "ba" on the screen, will be forced to backspace twice and then do the 3 taps (faster) to obtain the c. This is a total of 8 keystrokes to obtain one letter, and puts pressure on the user to type faster than their natural rhythm. A timeout imposes a universal minimum tapping speed when entering a letter.

A timeout period that is too long means that users need to wait between pairs of same-key letters. Thus users can type rapidly in some situations, but must be conscious of same-key pairs and deliberately pause between these. This increases cognitive load and creates an inconsistent user interface.

The last of these problems is commonly partially alleviated by providing a timeout kill button which can be used to immediately end the timeout period. Thus a user wanting to rapidly enter "no" could type 6 6 (kill) 6 6 6. Though allowing faster text entry, the timeout kill button does not relieve the user of the burden of anticipating same-key letter pairs. Moreover, the system now has an extra key. So in fact the "extra" Next key in LetterWise is not extra at all when compared to the vast majority of multi-tap systems. People who enter text rapidly with multi-tap are already accustomed to using an extra key.

2) Smoother, faster text entry

A separate Next key makes sense for smoother text entry because one does not have to consider same-key letter pairs. Text entry is also faster because fewer keystrokes are required and/or waiting for timeouts is not necessary.

Consider entering the word "babe" using LetterWise (LW) and a multi-tapped LW, with and without a timeout kill:

LW: 2 Next 2 2 Next 3 (6 keystrokes, no wait)
mLW (with timeout): 2 2 Wait 2 Wait 2 2 3 (6 keystrokes, two waits)
mLW (with timeout kill) 2 2 Kill 2 Kill 2 2 3 (8 keystrokes)

In the first case, LetterWise is faster as it requires no waiting, in the second it is faster because it uses fewer keystrokes.

3) Simplifying the user interface

Not only is LW faster than either of the multi-tap variants, it is also less complicated for the user. This can be illustrated by writing down minimal instructions for producing the correct letter after the first key press in each of the systems:

LW

Check if the letter is correct.
If so - go to next letter.
If not - hit Next until the letter is correct.
- go to the next letter.

mLW (with timeout)

Check if the letter is correct.
If so - if the next letter is on the same key, wait.
- go to next letter.
If not - before the timeout has expired, hit the key again until the letter is correct.
- go to the next letter.

mLW (with timeout kill)

Check if the letter is correct.
If so - if the next letter is on the same key, press timeout kill.
- go to the next letter.
If not - before the timeout has expired, hit the key again until the letter is correct.
- go to the next letter.

4) Making error correction simpler

Consider the situation where the LetterWise user has not hit the second Next when entering the word "babe". The screen will display "bace". To fix this, the user backspaces once to the c, hits Next, and thus fixes the problem.

In multi-tap systems (including a multi-tapped LetterWise), the user can backspace to c, but hitting a 2 again to correct the problem, results (with multi-tapped LetterWise) in the string "bacce". The timeout has long since expired and the system inserts a completely new letter. The multi-tap solution therefore requires erasing the incorrect letter and re-entering it. In a multi-tapped LetterWise, this is particularly bad because one may erase a "c" and then the first tap on the 2 key brings the "c" back, which must then be altered with Next. Thus three keystrokes are needed for correction, whereas LetterWise requires just one. Multi-tap can get around this problem by having insert versus non-insert modes that determine what happens in this situation. This adds to interface complexity and is completely unnecessary in LetterWise. In LetterWise it is clear when the user wants to insert a new character (they hit a letter key) or make a change to an existing character (they hit Next).

5) A smaller, simpler product

LetterWise with a Next key is smaller and simpler. The code base does not rely on the implementation of timers, which allows much greater portability. This means faster OEM integration, availability in more resource-constrained devices, and a simpler API.

6) Put the infrequent action on a separate key

In multi-tap, the infrequently needed action is to cancel a timeout period. The timeout kill is located on a separate button. In LetterWise, the infrequent action is to use Next to obtain the next most likely letter. The Next key is better located elsewhere so the user can get on with the frequent action (entering subsequent letters) at any pace they like, without having to consider timeouts or same-letter pairs.

Next is used on approximately 14% of all keystrokes in LetterWise (in English). Making LetterWise use a multi-tapping Next approach would save the user from hitting a separate key on these occasions. But it would introduce the need for a timeout kill key, and this is hit on approximately 10% of letters. The saving is therefore small and, as argued above, the problems associated with having a timeout are many.

7) Product testing

Informal product testing has shown that a multi-tapped version of LetterWise is considerably worse that LetterWise with a separate Next key. LetterWise was originally designed and implemented with the multi-tap approach, but proved awkward to use. Moving the Next functionality to a separate key solved these problems described above.

Tests at other companies have arrived at the same conclusion. Using the LetterWise API it is possible to implement the multi-tapping approach. When this has been done, it has invariably been concluded that a multi-tapping LetterWise is not viable.

8) LetterWise is not multi-tap

People who use multi-tap are used to tapping repeatedly on a key to obtain the letter they want. It is true that these people, if unaware they are using a new product, will find that their first keystrokes using LetterWise do not produce the expected result. On the other hand, first-time LetterWise users who have used dictionary-based methods will not find this surprising at all. These people may be surprised as they enter the word that the letters in the display are not changing at every keystroke, or that at the end of their word, they do not see the word they thought they were typing suddenly appear.

It is well worth having users face a very minor new task (hitting the Next key) to obtain the many advantages of LetterWise over multi-tap. It is an error to try to replace multi-tap with another multi-tap. LetterWise was explicitly designed to eliminate the problems of multi-tap, not to reproduce them.