OP I had a similar problem until recently. Shoot 'em up/bullet hell games didn't appeal to me. I came over this once I gave one series of games a try when I got a sega saturn earlier last year.
I got into the games just for the sake of cute girls and was heard they were big deal Saturn games, so I gave them a try. My first attempt was a test, and my second try a serious attempt at completing it. The game was Cotton 2 Magical Night Dreams, an arcade port based on the saturn's arcade hardware equivalent. It caught my attention for the cute graphics, kept me interested with the great music, and a refreshing sense of simplicity and purity of design. As I got farther, game overed a few times I started experimenting a bit and got to figure out the secondary mechanic to shooting in the game, the grab function. Upon figuring out how to use it in the games mechanics and work with the games design, it really clicked with me.
Cotton 2 is kind of a "cuhrayzee" shmup, to give you some ideas by comparing it to modern gaming language. It's a game all about pulling off and maintaining absurd combos both for game play reasons (balancing your combo to maintain control over the screen and to succeed in a level is a challenge on its own), optimizing movement, understanding the elemental properties of your attacks, bombs, shots, and knowing when to pop a combo for your own advantage. It's a really engaging game and its built around a fascinatingly enjoyable style of play.
I can partially vouch for how it emulates(decently after you run it the first time), although if you have the original hardware you will enjoy yourself more, it made me realize what makes shmups so fascinating. They're incredibly simple and extremely enjoyable because they test your most basic understanding of mechanics and add in a few simple mechanics that augment your understanding, they give you a pure sense of enjoyment.
It's not like a first person shooter where if the aiming has a weird mouse filter on it it's not right, or if the aiming is solid but the movement feels a little clunky because some objects in the environment awkwardly collide with your movement bounding box, it's a series of games defined by controlling a cursor and understanding the spatial movement of projectile shots and observing simple enemy patterns which can be summed up with basic shapes, cosine/sine, lines, etc. Because of the simplicity it's appealing, but because of how they indulge in the simplicity, somewhat alienating when you see a screen full of bullets and it looks like an impossible joke game.
I'd suggest playing Cotton 2, try the sequel Cotton Boomerang, try the first game on Turbo CD Cotton Fantastic Night Dreams. Very simple but core level STGs. Try Ikaruga as well, it's so simple but the brilliance is in the design.