I think the app itself should be installable through bluetooth.
if another user doesn't have this app installed,
the app should be able to transfer its apk package to the user via bluetooth.
I know it's probably an unpopular opinion, but I don't believe that we should be distributing APKs outside of the Play channels. It takes us back to the PC distribution model, with all of the associated security and usability problems.
It doesn't allow you to easily get at apks you've downloaded from the Play store, if that's what you mean, but I think that's just an anti-piracy measure. An apk you've downloaded from somewhere else is, as far as I can tell, just another file. I can't imagine why (or how!) it'd stop you from exchanging them, particularly if you have some sort of custom Bluetooth client.
Does it really try to stop you?
Not allowing apks via bluetooth seems like a usability issue too.