I see no comparison to a player folding in turn when facing a raise and folding if action is checked to that same player. The player that announced raise is commited to raise, period. Would you consider a different answer if the game were limit? I think you would...what is the difference? Knowing the amount? If so, why?
Then we may have to disagree.

But for what it is worth, I know a few TDs that would probably agree with you. Hopefully though, you will keep a bit of an open mind, and let me try to persuade you otherwise.

Personally, I think this amounts to a breach of etiquette, and I treat it as such. In a lot of cases, it is probably not a big deal so no warnings or penalties are warranted; but in other cases, it can drastically alter the way the hand plays out. It is notable that Robert's Rules states that as a matter of Poker Etiquette:
"Making statements or taking action that could unfairly influence the course of play, whether or not the offender is involved in the pot" are improper and grounds for warning, suspending, or barring a violator.
What do you think about this NLH situation?
Player A is in the SB and is chip-leader. Player B is in the BB and is short-stacked. Player C is on the button and has a large stack, but is covered by A. Post-flop, Player A bets and Player B calls. Player C has made middle pair, and is contemplating a raise as a squeeze play. Now...
a) Player C announces "raise" and is contemplating how much to raise. He is wary of Player A playing back at him, so he decides to raise a typical 3x the bet, intending to fold to a shove from chip leader A but call a shove from B. A actually folds, and
B closes the action by making the call, intending to see one more card with his straight draw. B hits his card on the turn and ultimately, excitedly doubles-up through C.
b) Player C announces "raise" and is contemplating how much to raise. He is wary of Player A playing back at him, but thankfully, player A folds before the amount of the raise is decided. Now, with Player A out of the way, Player C faces no risk of elimination and goes all-in to put maximum pressure on short-stacked player B.
B now folds his straight draw to the all-in bet, not having the odds to call and/or not wanting to risk elimination on a draw.
Comparing the two situations, I believe it is quite unfair for A to get out of the action prematurely here, by not waiting until C has announced his raise amount before folding. A's presence in the pot alone provided some protection for B by tempering the degree to which B can be aggressive; however, A's premature fold has opened up the possibility for C to go all-in against B,
an option that C likely would not have exercised had A, as chip-leader, not stepped out of the way. B is directly affected because he is now facing an all-in bet that he cannot call, even if he would have called a smaller amount that C might otherwise have raised to. If I were B in the second scenario, I would definitely feel that A's failure to wait until the raise amount was decided upon before folding gave C a huge, unfair advantage.
The difference between limit and no-limit is this: In limit, once "raise" is announced, the amount of the raise is already determined because it is absolutely fixed -- the amount of chips that must go into the pot is pre-determined by the betting limits in effect for that betting round, no more and no less, and so in that sense, simply saying "raise" can be considered a complete, well-defined action. In no-limit, however, once "raise" is announced, there can be a wide range of possibilities for raise amounts -- from a min raise to an all-in --
that will have varying effects on subsequent action and therefore, the raiser's action is not fully-defined in the same way as it would be in a limit game until the amount of the raise is decided.