I just tried it here...nope, cut/insert time doesn't do anything to alternate playlists.
One thing I do if it's just a couple of tracks that have playlists (like say the vocal and the lead guitar), you can create mono track for each hidden playlist... then move the playlist onto that new track (using "other playlists from the menu)...do your editing, and then switch each track to its original playlist, move it back to it's original track (using other playlists) then delete the new tracks.
it's kind of a pain in the butt to have to do that, but I can see why it doesn't alter other playlists. For post, it is really good to do your conforming on a duplicate playlist that way you have each cut list on a separate playlist in the session.
But...usually I try to tell clients to make critical changes like removing a verse either in preproduction or right before we go to mix. That way you're not dealing with playlists out of sync. But if you have to, moving the playlists onto other tracks can work fairly quickly for you.
William also mentioned that editing playlists should work like editing analog 2" tape...I would have argue that it does work just like 2" as it is now!!!! Think about it....
Each playlist is like a second 2" machine that's sync'd to the first 2" machine or sync'd to some sequencer using SMPTE. Each time you switch to a new playlist it's like taking one reel of tape off and putting another reel on. If you edit the first 24-track reel, you can't expect the second reel to automatically be adjusted just cuz they were in sync when you started. Nope, you have to also cut the second reel as well! Playlists are the same way.
Think of it this way...you've tracked the band on 20 tracks of a 24-track 2" reel...you know the vocalist is going to take at least 8 tracks for the lead, so you stripe a second 2" reel with SMPTE and sync it to the reel with the band on it. You do 20 tracks of vocals!!! You come up with a roadmap for your comp and you automate it. Then you record that automated version back onto track 21 on the reel with the band. Two days later the band decides to have you cut the second verse out...so you edit the 2" reel (hopefully a copy of it) and you cut out the second verse. Then a few days later the singer decides he doesn't like what he's singing on the outro and wants to use a different take...you put the vocal reel of 20 tracks back on the second 2" deck and wadda ya know!!! It's out of sync!!! Why, cuz you never cut the second verse out of the vocal reel, just the band reel. It's just like the way Protools works when editing using playlists!!! How 'bout that....Protools really does work similar to 2" tape after all.