There's no inertia while shooting
Sure, but you also move too slowly for some situations while doing so.
I don't know of any traditional shmup that is taken seriously that has inertia. While "other games do it" isn't necessarily a reason to do something, the reasoning for it in this context is very solid. Honestly, I consider inertia in a shmup a cardinal sin. Your game has unique mechanics, but the bullet dodging is fundamentally the same. Avoiding damage with precise movement is life and death. I really like the mechanics but I couldn't really enjoy the game if I end up dying due to imprecise controls. That's my point of view.