Question: Can one not do the repeated resets with civil suits?
Assuming you're referring to procedural delays, there's plenty of ways to delay in civil lawsuits but the overall time cost is nowhere near as much as in criminal prosecutions. The Texas Attorney General Ken Paxton has been under indictment since 2015 and his trial is set to start in April 2024.
Paxton's 9 year delay is a very extreme case of delay tactics but just keep that in mind.
Taking her story to law enforcement would definitely be sufficient in opening a criminal investigation, but those inherently take a lot of time even if they're given hard evidence (see the Trump or Hunter Biden investigations). Subpoenas take time, interviewing witnesses takes time, some might not cooperate, ...
So you're already starting off with a long timetable, which in these types of cases often doesn't result in charges being filed at all. The prosecution may have doubt if they can meet the criminal burden of proof and decline to file charges. If the investigation does lead to an indictment, that's more ways for procedural delays and a conviction is far from a guarantee regardless of the evidence. Rich and famous people get off on abuse cases all the time.
Civil cases are less prone to delay, but more importantly the burden of proof is lower. You're much more likely to win this case in civil court than criminal court.
This is just my personal belief but based on how Diddy operates, I think Cassie and her lawyers were fully expecting Diddy to immediately try to settle and kill the story.