For the Olympics, the 4 x 800 would lack competitive depth and be a scheduling nightmare.
To be consistent with the rest of the relays you would need to allow 24 teams to qualify and run 3 prelim heats taking top two 2 from each heat plus next 2 fastest as time qualifiers. The world record for the 4 x 800 is 7:02. Set the qualifying mark at 7:20 and how many countries could achieve that mark given a two year window? Kenya and the US for sure. Probably UK, Australia, New Zealand,Ireland, Canada, Uganda, Ethiopia, Poland, France, and Russia. Not Many more outside of that. If you changed event to a straight 8 team final taking top teams by time that would help but would be a little odd for Olympics.
The best teams on paper would almost certainly be Kenya and the US. However, the best 800 meter runners likely wouldn’t participate in relay because they would be smoked from 3 rounds in the open 800.
Even if you got 8 decent teams with a few stars mixed in it probably wouldn’t be that exciting. 4 x 800s at world relay events are generally a snooze fest with blow out wins. It would be awesome to see 5 teams take the bell within ten yards of each other but it just doesn’t happen very often.
For the NCAAs, the 4x800 makes more sense but I think it would have to be an 8 team finals only field. That said, I do think they should eliminate either the 5k or 10k. To be honest, I think a road 8k (50 man field) with final 400 on the track would be more exciting than either the 5k or 10k. They can show the race on the stadium screen while other events are ongoing then have a big stadium entrance for the finish. Have primes at 3k ( 2pts and 1 pt) and 5k (4 and 2 points)