Should a character be forced by circumstances to do something he doesn't want to do?
If you are a writer, it's an excellent thing to do.
One reason for the common fail, fail, succeed pattern in fiction is that the hero takes two tries before he's willing to make the commitment that will actually bring him success.
A writer wants to box his character in, whittling away his options, until he must undertake the drastic actions required.
Those are the things that bring about character arcs.
Especially if it means, say, sacrificing the legacy sword that he prizes, or going to the location that terrified him since childhood.
Not to mention that the dramatic and risky climax should be taken in face of all other options being ruled out. The Evil Overlord has built a tower that will collapse if the Evil Overlord dies? But, alas for his slaves, he will take everyone in the kingdom captive if he lives until midnight. Let us hope the slaves have the wisdom to flee. Those who stay, out of fear or desire to kill their overseers, we can not help.
The DM is more likely to find the players sending their characters charging for the tower before even finding out that it will collapse, and ignoring all sorts of elegant ways planted to let them bring it down more easily.
Or preparing it by fighting so many monsters, even ones more terrible than the overlord, such that destroying the overlord and the tower are trivial in the end. (And the land suffers all the while under his heel.)
Or perhaps ignoring the tower entirely to haring off after some random piece of background noise. (Much depends on the players and DM of course.)
Disabling this is known as railroading, and is justly hated because it snatches away player agency. The players want to do things, not sit on a train while things pass by.
Similarly, a writer can set up one and only one solution to the problem, and make it a puzzle because he knows he can endow the characters with the wit to find it and the will to search. (Rhetoric is needed to disguise this, of course. Thinking yourself back into ignorance.1)
The same can not be said for PCs. I have known players to sulk at the presentation of a puzzle and not even try to solve it, expecting a clue to fall in their laps.
Depends on the players, of course. Some are willing to cast about searching for clues, and a DM who knows his party can reasonably set up a situation with clues to the right way to do things, though the DM has to avoid setting it up in a way that one failed skill roll will prevent the resolution.
And going after the characters personally can cause real problems.
Some DMs and players work with it. I have heard of a DM who, in character creation, asks the players what sort of character arc they want their character to have. If the players can manage the personal detachment, the aesthetic distance, to regard the destruction of the prized enchanted sword as a necessary step in the character's growth, they can have great fun as the character learns to develop past that.
For a writer, a degree of aesthetic distance normally comes for free. More or less. The reader may be heart-broken when the young hero loses the enchanted sword he won in his first great conflict, but not in the same way as a player would be. Besides, the reader knows that something better is likely to lie ahead, in a way that a player can't. Such is the structure of story.
In My Ending Is My Beginning -- I Hope
You have it in hand, the triumphant ending, the glorious way the hero will defeat the villain and usher in the age of gold where he can marry his love interest in peace.
I wonder if there's a mechanics way to try to build in fail-fail-succeed patterns into D&D. All I can think of right now is a lowering bar for succes each time something fails.