I would like to be able to buy an Oyster reader (similar to that used
by inspectors) so I can check that my Oyster has been processed
correctly after boarding a bus or tram.

The problem is you have no proof that you have paid - at least if I had
an Oyster reader if I see a problem with my card I can try to validate
my Oyster Card again.

Just think what could happen with a contactless system to read the data on
the card , when it falls in the hands of those using it for fraudulent
reasons..
Just mingle in an underground train with the punters, and obtain all of the
personal data stored on it... sounds pretty horendous. I doubt if you will
ever have an oyster card reader...