I don't miss tape because I still have a 2" 16 track at my disposal.
There are a LOT of things I miss about the era, some of which are directly related to tape, all of which were probably already mentioned:
1) I miss the discipline that tape enforced... you did not make edits unless you really needed to, you did not keep every take, sometimes you had to commit to specific effects or bounce-downs... all of which had the effect of making you think, a lot sometimes, about what you were doing. And yes, I think that it could lead to better output.
2) I miss the time it afforded - you had to wait while the tape was loaded, you had to wait for rewinds, and so on. And in that time you had time to chat.
3) I do miss showing off - window edits, spot erasing... this could really make folks nervous.
4) for whatever reason, I miss sitting back with my feet on the console watching the reels spin while listening to that "final" mix.
5) I do miss being able to fix whatever went wrong... my JH16 has no microprocessors!!!
6) more than anything, I really miss people learning to LISTEN to their edits. I've watched folks make edits based solely on the visual representation on the screen, and as often as not, maybe even more often, those edits do not sound as good as they could... if only the person had really listened. In fairness, there are no software tools that I've used that provide a true equivalent to audible scrubbing, although I am getting better at using the available tools...
7) while there are computer based studios that still have enough space for a band, I miss working with bands, because my current place doesn't really have the space. But that's more a matter of economics than just the presence of a washing machine sized tape deck.
I do not miss transports eating tape. I do not miss cleaning them, I am on the fence about aligning them - there was a certain peacefulness that came with completing the job. I do not miss the space they take up, or the cost of tape, and of course the noise and other audible artifacts are gone, and everyone one likes that.
In the balance I'm quite happy to have the tools I have, but we did lose something in the transition.