I think people were pretty tired of the war in 1945. The idea of stockpiling aircraft might not have looked as appealing as we see it. Also, since the war production had eaten almost all resources, scrapping and reselling was better business.
There were private collectors too. Many private museums started their life at a cheap post-war sale, but most were sold to be scrapped (it was part of the deal, as states don't like to arm citizens too heavily).
I have a pdf (a bill of sale from 1946) with a list of HUNDREDS of aircraft, sold to a private company for $55.426,68
Including P-51, P-47, P-40, P-39, B-24, B-25, B-26 and PBY.
Drop me a PM of you would like a copy.
I'm not sure why such sites are not investigated, but maybe there are a limited number of people who can fund the recovery/restoration. They do actually recover a few each year.
A sunken JU-52 seems like a perfect bird to investigate. Chances are its kinda intact (not crashed), so maybe you should find some more information. I'm in Denmark so its only a short drive away
Regarding the Stuka: Thats what a Stuka looks like, here is another pic.