This has been a good example of a common pitfall in modeling. The error
made in this case was to attempt to apply an unsuitable model (a voltage
source in series with a resistance) to a system to be modeled (a
transmitter). As the OP showed, the attempt leads to an impossible
result. The classic example of this is the "proof" that a bumblebee
can't fly, based on a flawed model and immediately shown to be false by
simply observing that they do, indeed, fly. Yet we see people falling
into this trap daily, not only in modeling electrical circuits, but also
in modeling such diverse processes as human behavior, economic systems,
and roulette wheel numbers.

Unfortunately, the bad results of applying unsuitable models aren't
always so obvious as they were here. So it's always wise to check to see
if the model fits before putting faith in the results.

Roy Lewallen, W7EL