I suppose I consider it more of a core design problem. But not a major one, rather a very fixable one. The odd part about it now, in my opinion, is that the natural inclination is that shooting down will make you go up. But in this case, you shoot up and that prevents you from going down. It kind of breaks the mental model of "the gun has force that pushes against my character". I would try to hold that concept as a central premise, and then build upon it. Imagine if shooting an enemy below you pushed you up more than shooting the ground. That is the sort of thing that can really emerge, and the player can add it on top of their understanding. Like, "ok my gun pushes me away. lets try shooting down. oh cool, that makes me go up! now let me try hovering with it and shooting an enemy below. oh wow, that makes me really go up!". That is the type of coherent system that is fun to experiment, and learn the nuances of.
Also, because it is a side-view game with gravity, going upwards is an extremely common need. It really should be quite simple and smooth to happen, and be easy to accomplish almost immediately for any reasonable player. That's because it's simply not fun to be floundering around trying to "move up". Mastering that doesn't feel good, because it's not cool or flashy or that interesting. Imagine in a 3D game, if climbing a ladder required some timing mini-game, and if you messed up a little bit, you crashed back to the ground. On this point, I would honestly consider just making it so that shooting down make you move up. There is a lot of play in such a system, because when you are trying to "super jump" with your machine gun, you're not shooting enemies. Also, it leans into the theme of "never stop shooting". There could be a lot of play and nuance in such a system, like, at what point after you jump is it optimal to start shooting? How little time can I spend shooting and still get to where I am aiming?