@Rigwyn
1. That's what windows are for. Also, closed doors keep the warmth inside, with the fireplace and all. They also keep the bugs and dust outside.

2. Do you mean that the captain of the guards is charged with guarding a tavern? That's what bouncers are for.
3. It wouldn't be a pita or all in game doors would always be open. Anyway, the closed doors was an alternative, not the only suggestion.
Swinging out doesn't give more room inside, if the doors were opened to the extremes of the walls. Keeping the doors stuck outside and in the middle blocks what is apparently a wide entrance, not to mention the wind would likely slam the doors into each other producing an annoying noise each time. As for bashing the doors in, you could brace the doors from the inside (with chairs and tables) pretty quickly, so even if the lock is compromised, it won't be easy to do, unlike pulling on the doors. And if you're not around to brace the doors, then picking the lock, sawing through a bar, chopping the doors with an axe or just bashing it in won't stop someone determined from doing so. Besides, didn't you mention the guards outside?
EDIT: There is also something called a
"lock-in" in some places that has a use for locked doors instead of relying on guards outside.
...a “lock-in” occurs when a violent, or potentially-violent patron is removed from the premises, and the doors are deadlocked to prevent the individual(s) from re-entering, and to prevent patrons inside from leaving for a short duration so as to prevent contact with aggressors (as a measure of duty of care). During the lock-in period, it is often a traditional courtesy of the venue to provide free drinks and snacks.
The game's setting and immersion don't change anything in this case. If they do, I'd like you to point out which part of the settings makes a difference here. In fact, because the game doesn't have the best collision detection, it is better that the entrance is wide without the doors stuck in the middle in a funny position. And this is based on playing the game, not real life.
@Thoss
Not at all. The doors can swing either way, depending on an establishment. If the doors swing outwards, the entrance is typically inside a niche or an arch of some sort, so that an open door doesn't block a walkway or a road outside the establishment. Otherwise, such doors usually stay closed, and return to a closed position after someone opens them to walk in. In case of fire, taverns aren't a bus or a train. Not to mention it would be easier for some perpetrators to trap the crowd inside by bracing the doors from the outside. There are also usually dedicated emergency exits, not to mention windows. Here are a few examples of taverns/pubs with the doors swinging inwards:
The Williams Arms, near Braunton, North Devon, EnglandThe Eagle, City Road, Islington, LondonThe Eagle, Clerkenwell, Londonetc.
There are also types of doors that can swing both, inwards and outwards.
Whatever way the doors swing, they should not be blocking the middle, if they were meant to be opened in a wide entrance. Even if the in-game verion was an entrance and an exit side by side, it still looks awkward.