AFAIK, detonating at altitude is done for fallout reasons. Detonating at the ground would make the fallout much worse.

Airbursts are generally used to maximise the area damaged at the cost of peak damage - so for soft targets like cities. Ground bursts would be used for hard targets (deep bunkers, missile silos) that are relatively small but hard to kill. I suspect in wartime fall-out wouldn't be a major factor in planning all out attacks whereas it was a big factor in atmospheric testing.

I also wonder how dangerous fallout was considered to be, in the long run. I have the impression that up into the late 60s fallout was considered dangerous in the short term but not after say a year.

There are rules of thumb like the 7:10 rule:

https://emilms.fema.gov/IS3/FEMA_IS/is03/REM0504050.htm

Long term effects are tricky because of biological processes concentrating some elements (I think mainly calcium, iodine).

Of course, if you want to get really nasty you can salt your bombs with appropriate elements (notably cobalt) that have long lived nasty isotopes:

https://en.wikipedia.org/wiki/Cobalt_bomb

Interesting use of the word "worse".

Noted. Could come in handy at some point!