It depends on whether you think saving can be abused to make the game easier than it's meant to be or the idea that checkpoints add an "artificial" layer of difficulty.

I think since you bought the game you should be able to save whenever you want. But another part of me sees the potential abuse of that and thinks that you should be limited to max 3 saves a mission/level.

That way you can save if there is something you NEED to do that pause won't cover but it's still difficult.

Also I think games should ramp up the difficulty the more often a player saves. Get good at the game, master the controls. Don't use saving as a workaround for beating a tough mission! Get good at the game.