That’s a pretty big “only”.

Airplanes normally don’t fly so close.

There are many situations in real combat where pilots need to fly even closer than typical air show formations, like refueling or escorting other aircraft. So close formation flying is a fundamental skill for a pilot. Sure, we can minimize risk by not using certain aircraft and close formations during airshows, but pilots will still need to train and execute missions using high(er) risk maneuvers. Also air shows are probably not the largest portion of flight time for a pilot.

Formation flying usually involves getting close and then 'just' maintaining distance. This has nothing to do with formation flying, this is acrobatics, different ballgame

Fighter jets in training probably do?

Doubtful there is any acrobatic training like this for the regular fighter pilot.

You don't need to do some rigorous searching to find that military jet planes do not need an airshow to crash. Just search f-35 crash