Solid state amp: Ok with no load. Tube amp: not ok.

Very few tube amps had this problem. Only some that weren't stable without a
load.


That's not completely true. The TDA7293's are designed to work more
efficiently with a certain load. By not having a load you reduce the
efficiency and it gets warmer.

"Efficiency" is meaningless unless the amp is actually driving a load.

Without a load, the amp is drawing only its bias current. Which, for most
amps, is not very much.