It is pity! Is there any other way to get rid of this shortcoming?
Instead of deleting, create a folder called "recycle" on the flash
drive and just drag the files there when you want to get rid of them.
There is one thing you might try. I had the "My Documents" AKA "users"
folder pointed at a network drive for a while. Windows decided that
because of that that it was a "local" drive. It put those files in the
recycle bin for me when deleted. (I also recall that it searched the
network drive as a local drive when I did a search and treated it a
little differently in other circumstances too). I don't see any reason
you couldn't use a flash drive in the same way.
Keep in mind that if you do this and the flash drive is unavailable,
odd things tend to happen. Not "irrecoverable" things, but, for
example, programs that store settings in those folders will get
annoyed when you start them and the folder is not there. Some get
really annoyed, others just a little.