I’m pretty sure I don’t want to allow saving at any time from the main menu.
... why? Don't you use a game engine that would handle this type of clerical work?
Sure, that is a design choice. A bad one in many cases. It is artificial difficulty. For that Resident Evil game, it added another meta layer to the horror. You were facing the real danger of needing to redo the level (and RE is old, so they technically could not save every place back in the day).
Ability to saving a game's state is a meta option. It is not part of the game. For the player it is a quality of life feature, like being able to configure controls.
If you implement saving restrictions, you need to be careful to implement them in a way that it adds to the fun and is not seen as lazy difficulty increase.
A typical restriction would be to not being able to save inside combat or while doing certain puzzles, but allow free saving while doing exploration.