DLR ticket machines aren't that unique - the Tramlink ones are of the
exact same design!

Indeed so, as are most of the ticket machines on the Paris Metro -
which have recently been adapted with smartcard readers for the Navigo
card. So it can be done!

It would be really useful if the DLR machines did do Oyster - I was a
bit stumped the the other day with a friend who needed to top up their
Oyster card before catching the DLR at Shadwell - the nearest place we
could find was on Commercial Road.

It does seem a massive oversight to me, when TfL is trying so hard to
promote Oyster as a replacement for all paper-based tickets (which it
blatantly isn't, at least not yet!)