I got my first tape recorder for Christmas when I was 8 years old. (My dad had a WIRE recorder when I was a toddler.) I used tape recorders professionally in studios and radio stations for decades. I don't miss them.
The OP asked for specifics, so...
Although I became a pro at editing tape with a grease pencil and a razor blade, the occasional bad edit was difficult to piece together and try again without a blip in the sound. Similarly, if a razor blade became magnetized, (which would happen naturally if a blade had been used a lot), every edit would have a blip. Knowing how to edit well with tape certainly informed my ability to edit digitally, but I'm glad I don't have to buy splicing tape, blades and grease pencils. Also, the Undo button is a blessing.
I like what tape did for the sound of certain instruments, but the hiss was always annoying. Today's tape emulations do a great job, including X3's built-in emulation. UAD's Ampex ATR-102 with 456 tape sounds exactly like the real deal to my ears. And I can turn off the noise!
When I'm working on a project alone, I don't miss rewind time. I must say, tough, that rewind time was always a moment for the band to have a quick discussion on how to improve the next take. I keep that thought in mind when recording others, so even though all I've got to do is return to zero and start recording again immediately, I usually give talent a little bit of time to get their heads together before saying, "Here we go again" and punching Record.
There are plenty more reasons to not want to go back to tape...like keeping heads aligned, making sure bias is set correctly for each individual tape formulation (you couldn't just swap to a different kind of tape without resetting bias), keeping alcohol & q-tips handy for cleaning heads...and the high cost of tape. The rock station I programmed was the first in my town with digital multi-track in the commercial production studio, and my main selling point to management was that we could quit spending hundreds of dollars a year on tape, eventually paying for the new digital studio.
I miss the tape recorder like people missed the horse-and-buggy after cars were invented. It was fun, but this is WAYYY more fun.