Half Life 1 for example launches its rockets from the weapon, not the players eyes.
Pretty much all space action games (Freespace, Wing Commander, X-Series, No Mans Sky etc) also launch their projectiles from the spaceships muzzles.
Many third person games like Dead Space do the same.
And yes, if there is an obstacle in the way, the projectiles will hit that obstacle. Yes, it can be an issue, mostly when the obstacle is right on front of the player character but you try to shoot over that obstacle to an enemy. It can be a negative thing (“if i point my mouse at it, i should hit it”) or a positive thing (“instead of just pointing and clicking, the player is rewarded for being more aware of his surroundings and projectile behavior”) and a realistic thing (if i hold a minigun at knee height, have a shoulder height wall in front of me, it’s realistic that the bullets hit the wall instead of what i’m looking at")…
It all comes down to whether you want to make it realistic/immersive (spawn from muzzle) or more action/arcade-like (spawn from players eyes).
That being said, Dead Space handles this problem really well by having a visible laser sight ray pointing forward for each weapons muzzle, so the player can see if any of the weapons muzzles is obstructed by obstacles.You can take a look at this video for examples:
