I never really understood that. 110 is 110 I always think transformer or not...
The big difference is the ground return path. If you have 110V from a transformer
supply then you can accidentally touch one side of the circuit and not get a shock
because you don't complete the circuit to the other side of the source. But with
a transformerless supply any path to ground acts as a return, and you can get a
nasty shock with the return through your shoes, for example.
Inserting an isolation transformer ahead of the transmitter solves the problem
because it isolates the rig from the AC ground. One way to do this is to use
a pair of filament transformers back-to-back, so you step the 110V down to
6.3V (or whatever) and back up to 110V. The power limitation is set by the
current rating on the filament winding.
Transformerless design was popular for domestic electronic equipment because
it was cheaper, but required a totally insulated case with plastic knobs and
no connected wires, etc. It generally isn't a good idea with things like ham
rigs, especially sitting on a bench next to a rig that is well grounded, either
to a ground rod or the ground conductor of the AC line, because if you happen
to touch a hot spot on the transmitter while in contact with the other rig or
a piece of coax it can be fatal.