Personaly i often find shooters to be either dull or average most of the time, doesnt matter much to me if first or third person. I think this may just be due to modern design approaches more than anything else, though there are plenty of bad older games aswell. I recall games like unreal tournament and raven shield being more appealing to me, than somthing like titanfall or even the new doom. Perhaps my tastes have changed since my youth, perhaps it's a little bit of both.
Since this thread seems to be somwhat covering the perspective as much if not more so than the game genre i'll chime in some extra thoughts.
Immersion in first person somhow being better.
Falling back on this argument always strikes me as a little weak, you can get engrossed with practicly any activity, reading a book as example and being drawn into the world, visualising the written world and giving voice to the characters as they speak. Listening to music and tapping your feet to the ryhthm or singing along to the lyrics.
Immersion is about so much more than simply being able to lift up coffe cup's ingame or looking down and seeing some legs, hell one of the most immersive game's i can ever recall playing was defintaly world of warcraft, that hooked me in and dominated my time at the pc and my thoughts when away from it, i entered that world fully and even now a part of my mind is still trapped there all these years later, i remember details about quests, about the things i saw for the first time. Immersion is inherent is all games and practicly every entertainment media.
The idea that first person is just better for everything.
This one is definatly in the purview of personal opinion but first person is actualy very limited for alot of gameplay styles. Though it may excell at shooters, climbing a wall in an action/adventure game would be rather bad if all you could see was the wall 2 inches from your face, i can't even imagine how a RTS without the tactical overview would play. (actualy i could but it seems substantialy less efficient, hyperbole is fun)