As I recall at the time, there was a lot of crying about a lack of a decent crime and punishment system, that it was too easy to get away with killing, especially in lawful systems, but as I also recall, a lot of it was aimed at PvPers being able to wander around in high sec systems killing other players with no real consequences.
I felt at the time notoriety was meant to target PvPers doing that, to push them to carrying out their business in lower security systems. I don't really recall any (many?) PvEers saying that crime and punishment needed fixing for PvE stuff.
And then the new system released, which barely bothers PvPers but is a royal pain in the jacksie for PvEers. I basically don't do lawless stuff at all now outside anarchy systems because its simply just an annoyance. Either that, or leave it to the end of the session then log off for the day to allow the notoriety to time out.
I don't know what FD's intention was, but from my perspective it wasn't an improvement.
I regularly gain fines & bounties from stuff like base assaults & killing politician missions but rarely do anything that gains me notoriety either, the time taken for notoriety to cool down acts as quite a deterrent to breaking the local laws as you suggest. I've set up some lawless assets around my territory then taken that asset owning local anarchy faction down below 7% influence so they won't lose the assets unless someone deliberately pushes them up to start a war too, because that allows me (and anyone else) to do things that might be against the law somewhere else in that lawless space. Ideally I'd have every asset but the controlling station be owned by the local anarchy but that's pretty hard work & one or two assets are usually as much as I can (be bothered to) do.
Before Notoriety bounties would last a while & I used to use that time to 'lay low' by going exploring so in that respect notoriety is a lesser punishment than what preceded it but still, it punishes breaking the law, not murder of innocents and not PvP unless someone commits a crime by doing it in lawful space. I helped put San Tu back to lawless ages ago (it's since been returned to lawful a couple of times) to help the PvP hub train players without needing to worry about notoriety.
I don't think notoriety or any of the C&P stuff adds much to PvP, it's just consequences for crimes that also captures crimes via PvP.
One of the issues with PvP fights is pre-emptive self defence, where the oppressor has not yet gained a bounty for assault or murder of an innocent (unwanted) player (or NPC). IRL pre-emptive self defence is allowed (self defence is an absolute defence in law & does not require the attacker to strike first eg they could threaten you with a weapon & you disarm them before they actually attack).
Notoriety is intended to be a consequence for breaking the law. That it's also acting as a deterrent to PvP first strikes (and pre-emptive self defence) is a side effect. I'm sure lots of people (possibly including some FDev staff) hoped it would act as a deterrent to ganking but I don't think that was ever an intended primary effect.
TL;DR I agree waiting for notoriety to cool down can be frustrating (it's supposed to be) but gaining it can be fun and avoiding it in the first place even more so
