I think that you want this to be a game it isn't. It's meant to emulate old school nes games and challenging difficulty that is also satisfying, fun, and rewarding. I find it so satisfying shooting down hordes of enemies, losing weapon upgrades creates more tension which I personally enjoy, there IS an auto fire option (just hold down the button), and the swarms of enemies are totally manageable with practice.
However, I agree that it's a bit too punishing. I will die on the hill that lives systems are not outdated and are good game design, but I think that they need to be done correctly. I find losing a life and then having to retread through the entire level really tedious. In my experience, the lives system doesn't really do much if you have to replay the level anyway. I've identified two courses of action here: if OP wants to keep the lives system as a way of offering a second chance, I'd add some checkpoints as you suggested so that they are valuable. On the other hand, if the player starting the level over is intentional design on the dev's part, I would actually remove the lives altogether and just have the game end on death.
I personally really love this game. I find it SO fun to try and keep my max weapon upgrade and plow through enemies without getting hit, and I love the frantic running away when I do get hit and lose those upgrades. I may disagree with you but really my problem is just that you gave all criticism in a condescending way without any positives or compliments. That isn't constructive criticism, it's just bullying.