So are DMs supposed to sit back a little more for the greater good?
I am not worried about the 5e idea of having different style of character builds at the same table. Whether a player wants a low-complexity fighter or a high-complexity fighter does not affect my DMing much, maybe not at all.
The DM must essentially be good at two things: (a) running the story (designing the adventure/campaign or learning it from a sourcebook, let the plot unfold dynamically depending on player's choices, bring good descriptions to improve feeling and immersion...) and (b) running the rules.
What really depends on the edition and which modules you are using is (b). It's possible to have a DM so good that she becomes familiar enough with all the rules and can easily use any module that the players are intersted to have in the game, but at least I know that I might have some difficulties. So rather than running a game poorly because I don't understand a specific module enough, I would really want to retain my rights to say NO, if I think it would be to everyone's benefit. The premise of 5e is to make this kind of DM's choices easier than in previous editions, and this is good.
So eventually the only problem I see with player's choices is if the player really wants to build a character around a module that I cannot run properly. Let's say that the player wants to play a fighter specialized in tactical movements around the battlefield and I don't feel able to run the game smoothly yet with such module, what do you think would really result in a better game? The DM backing off and running a mess of a tactical battles, or the player backing off and playing a different fighter? What is the greater good?
I don't think I'm particularly picky on what rules to have in the game, I'm rather more picky with fantasy elements that don't fit with the setting (I would like each of my campaign to have some difference, not be all kitchen sink).
But my bottom line is always to say, if you can't have this character in this campaign, you'll have it in the next. As a DM I can't always run what I want now, I have to make a choice for a certain campaign type to run and stick with it until the end, and leave other ideas for the next campaign, so why would a players absolutely need to play one and only one character concept right now?