The biggest reason why saving is only allowed at specific screens is because saving during sex/battles scenes or most importantly during map periods would require to save all the information regarding AI states, which would bloat the memory size of the save, which implies another plethora of problems due to how Twine manages its games' memory. I could also go on about how allowing to save anywhere discourages players from being careful about their choices, which is a more subjective discussion in which we could disagree, but given that the technical side has higher priority there isn't much point in that debate anyway. In any case, during the prologue you should have had two or three opportunities to save - if your computer removes files that aren't created manually, I strongly encourage you to use the Save to Disk option.
All of this aside, I'm glad about reading in your comment below that you're enjoying the game, even if there are QoL issues that hinder your gameplay session.