I have thoughts coming from a few different angles here. Let's see if I can make them play nicely with each other.
First, I'm going to put this right out in the open: I am not at all annoyed by the multiple Spider-Man reboots, and I don't think I ever will be. I have been a fan of Spider-Man ever since I was little, long before I ever saw him in a movie or read one of his comics. I can't honestly say why I've always been such a fan growing up (though there are certainly parallels; I've always been shy and nerdy and somewhat weird, and in middle school I did have quite the crush on a fun, outgoing redhead), but I have, and that deep and abiding fan-ship means that I want to see as much of him as I can. I appreciate all of the movies for the different aspects of the character that they focused on, and I can't wait to see what's coming next (though right now I have to say that I think Tom Holland is my favorite).
Now, does that apply to all superheroes (and, by extension, their movies)? Not really, no. Even before Batman vs. Superman started getting terrible reviews, I just didn't have much interest in seeing it. This isn't DC vs. Marvel fanboyism; for some reason it just didn't appeal to me. Even on the Marvel front, I'm a little fatigued. Three Marvel movies (Captain America: The Winter Soldier, Iron Man 3, and Thor: The Dark World) came out during my mission, and it took nearly two years for me to catch up on all three of them. I saw Age of Ultron and Civil War in theaters, but I didn't check out Ant Man until just a few weeks ago. I didn't go see X-Men: Age of Apocalypse, and I'm not sure I'll ever go out of my way to do so.
So you could say I'm a little burnt out by superhero movies, but I'm not so far gone as to boycott them completely. Honestly, it's just a little hard to stay invested when there are so many characters and plotlines to follow. Additionally, it just feels different than it used to. I remember back in 2008 when Iron Man first came out. People were like "oh, a new superhero. He's pretty cool I guess." Then, a month later, The Incredible Hulk was released. Before, it seemed like most people were thinking "A new Hulk movie? Wasn't there just one a few years ago? What's going on?" But then they saw the movie and they were like "WHAT? TONY STARK WAS IN IT? WHAT IS GOING ON?" I don't want to say that this sort of crossover was completely unheard of before, because something in the back of my head says it wasn't, but it definitely felt like something new and exciting. More movies came out: Iron Man 2, Captain America: The First Avenger, and Thor. Those movies helped build the excitement, but it's important to note that they weren't necessarily amazing on their own: Rotten Tomatoes reports their average critic scores as 72%, 80%, and 77%, respectively. Certainly not bad, but not the greatest, either. With that in mind, it suddenly became a big thing to see how The Avengers was going to do. It ended up being a smash hit, and the culmination of everything felt really good.
Since then, a little bit of the magic has left for me. These aren't exactly underdog movies now; the characters are so mainstream that it's almost a given that tons of people are going to watch them. Additionally, since The Avengers, there's been a lot more crossing over in between individual movies: Cap shows up in Thor 2, Falcon fights Scott Lang in Ant-Man, and the third Thor movie is actually going to be about both Thor and the Hulk. On one hand, that's great, because that's how things are in the comics: all of the heroes inhabit the same world and step into and out of each other's stories. On the other hand, it now seems like a ton of movie time is now spent setting up other movies. It's nice, but also a bit overbearing.
One other small concern I have is about the talent involved in these films. It seems like a disproportionate amount of acting talent is getting drawn into the Marvel or DC Universes. Again, in some aspects that's good, because it means that these characters are getting the attention they deserve and won't just be thrown away on some C-list actor. However, a lot of these actors are so good that I want to see them in things other than superhero movies, and it seems like that could be a problem going forward as crossovers keep happening. Specifically, last weekend I finally got around to watching the Sherlock Christmas special ("The Abominable Bride") with Mère Rubik. I liked it a lot, and I couldn't help but wonder if the next season was taking so long because Martin Freeman and Benedict Cumberbatch have both been swept up by the superhero movies.
In the end, I'll probably stick it out and watch all of the Marvel movies until the end of Infinity War. We've still got Doctor Strange, Captain Marvel, Black Panther, and Spider-Man: Homecoming, after all. When that's all said and done, though, I think I'd be fine if we all moved on as a society and explored other genres. There are so many interesting stories to tell, and as much as I love superheros and comics, I don't think they have a monopoly on quality storytelling.
P.S. Though superhero movies may not always be as popular, as humans we've been obsessed with the idea of men and women with extraordinary powers since essentially the dawn of civilization. I don't think that's going away any time soon.