5e ditched the rules present in past edition's that make going up/down in size from medium a mixed bag so size large is pure awesome with no meaningful downsides for anyone with an aura or pbaoe powers
It will indeed affect combat, and as far as I can see only in favor of the large creature. But it might also affect the Exploration pillar (your character does not fit through that door) and perhaps even Social Interaction pillar (this will depend on the players/DM).We don't have large PCs in D&D because the designers are simply too worried about their (martial) combat aspect, and that's pretty much it. It has little effect on the other two pillars, but because it skews the combat minigame, they won't allow it - even when said portion is only supposed to be 1/3 or less of the game...
Squeezing rules would handle the door problem. I would think an Orc, Warforged, Shifter or Goblin character would "break" the Social pillar long before a Large creature did.I think the main reason is that nobody in WotC wants to fix any problems in existing adventures that would occur if you get large PCs. The complaints would never stop if a large PC cannot get access to parts of a dungeon or find a particular clue. "WotC broke the game!" And it might be in a few words hidden in an adventure book. All adventures were written with medium & small PCs in mind.
It will indeed affect combat, and as far as I can see only in favor of the large creature. But it might also affect the Exploration pillar (your character does not fit through that door) and perhaps even Social Interaction pillar (this will depend on the players/DM).
As a DM, I would not allow it because it would constantly invite discussion. MY character is large, is it reasonable that I can see over the crowd what happens? MY character is large, so I can hit that flying creature at 15 ft altitude without jumping. But then I probably wouldn't allow centaur or minotaur PCs anyway.
You can - but the rules do not tell you to. Being effectively blocked from 5' wide corridors makes about half the dungeons part of dungeons & dragons inaccessible and really puts limits on dungeon designers.Plus you can run into that with races that are taller than humans on average anyways, Goliaths, Firbolgs, or Bugbears, for example.