Szczepan Bialek wrote:
Electrons escape from each charged body. Your antennas emit electrons and
for this reason they need the sink of electrons (the earth/chassis/
counterpoise).

Of course not.
Not only is this effect too small to be measured at voltages common
on a transmitter antenna, the voltage is also AC so these effects will
cancel out along the cycle of the AC wave. The net result will be zero.
There can only be a net current when there is a (large) DC voltage on
the charged body, which is not the case on a transmitter antenna.