I am usually a DM and are all-in on Option #4. I set up the game we are playing and those that agree to play will come up with characters that fit pretty snuggly into the baseline of that game.
And there are several very good reasons for this and why I do it the way I do.
1) Every campaign I run is different. It's rarely the same world twice, the styles of the campaigns are pretty varied, and on the the few times I return to a setting (like say Forgotten Realms) the adventure locale is far enough away from the previous one that there's little to no cross-over to worry about. And thus this means that my players know that if they desperately NEED to play a certain character and it doesn't fit the game we are going to do right now... they can hold onto the idea for the next game that comes up soon where it will.
2) My circle of potential players is rather large. As a result, they all know I have plenty of options to fill out my table and thus if I'm making a specific request for types of PCs... they know to jump in on my ideas with both feet if they really want to play it. They aren't going to waste their time or my time being wishy-washy about the theme and whether than can play something further outside of it because they don't
really want to embrace it.
And 3)... perhaps the most cynical reason of all and the one that admittedly puts ME looking in a pretty bad light...
...most players just aren't that good at roleplaying character (in my opinion).
What does that mean? It means that for all the hullabaloo about players having these grand ideas about these super-specific character concepts... oftentimes using all the bizarre choices for races and/or race/class combos, and backstories that make them out to be these esoteric and mysterious and out-there special snowflakes...
...when they actually get to the table, the way they play the game is almost exactly the same way they would play if they were playing a human fighter farmhand who picks up a sword and goes adventuring.
They just don't play differently. They play the same way regardless of who or what they are playing. For all the weird and wild choices players pull from any of the player-centric tomes out there with which to create a character... those basically become merely a bunch of different
game mechanics to use, NOT new ways to roleplay their character in any way, shape, or form. And anyone who knows me here on the boards knows... I care not one whit about new game mechanics.
The reason why two fighters in AD&D appeared different in play was because of how the players themselves roleplayed their characters with interesting and different quirks, foibles, wants, needs, hatreds and so forth-- NOT because they had different game mechanics to use (cause as we all know, an AD&D fighter pretty much only had their six scores, HP, AC, some saves, and a weapon choice to mechanically be different than another AD&D fighter.) The mechanics would not differentiate the two of you... your character's personalities and how you played them did it.
And because of this... in my game if you want your PC to be a special snowflake... you will have to
roleplay them as such. How your character integrates and reacts and dives into the story will create your special status, NOT what weird options you took when building it or what odd times you roll dice in whatever combinations you've found to do so. Thus as a result... you should not bother at any time ask me to play these weird combinations you've come up with (unless I have specifically said for the game that anything and everything was open and available.) Instead, you will impress me more by taking the gosh-darned most basic and typical concept for the game to make a character out of... AND STILL manage to create your special snowflake through playing that character
by being awesome.
But yeah... that's hard. And quite often, my players AREN'T that. Instead, their Tabaxi Outlander Sun Soul Monk ends up looking, feeling, and playing exactly as if they were playing merely a human warrior. So all their "really cool" options they went looking for end up not meaning a thing. So just don't. Instead, if I offer a small pool of options because I want the PCs to be forcefed into being within the theme I'm interested in running in... if you really want to play that badly, just go with it. Because if your roleplay ability is only going to fall within a certain narrow parameter anyway, I'd rather your character concept at least be right in the middle of what works for the game.