Tried the demo!
There's a small bug: when A is pressed during the death it doesn't fire on new spawn. Easy to recreate, just hold the A all the time and die, and you'll see.
But also, is there a reason not to fire all the time? Will there be the levels where you have to be careful when you shoot and when you not? If no - I'd recommend just auto-fire without pressing any buttons.
Good luck!