I dunno on how the PSP environment loaded using adrenaline get downloads form Sony servers so I can't answer on "why we can't download PSP and PS1 games using PSP Store on adrenaline".
But as to why we can't download Vita games even with activated vitas is that sony asks some data from the vita and it fails to respond accordingly because the answer changed between firmware versions (It wasn't checked before).
This process occurs with every vita download now, even on activated vitas. So activated vitas can't download legally owned games and DLC, deactivated vitas can't be activated until a new spoofing method is created and made public.
https://gist.github.com/yifanlu/c4cc12d3f1ccaebbf1846b84a69a4bfb
Maybe
@yifan_lu may know as to why the PSPemu shop environment also fails to download.