Thank you all around!

I went through a couple of display motherboards, and looked into the
specs of all power devices.

What their applications have in common is being rather high current
and low frequency. You don't find much rated to work beyond fery few
MHz, and with very large capacitances.

Examples:

- power MOSFET capable of switching 600V, 10A peak, with 2200pF gate-
drain capacitance

- bipolars that can absorb several watts, but no higher than a couple
of MHz

- horizontal finals yjat are included in fairly complex ICs with lots
of ancillary components in feedback and protection circuitry - at
least in CRT VDUs from the last 10+ years.

I have no doubt some RF can be teased out of these, but it seems to me
it would be at the price of major design complications.

The advantage of tube finals was that their high-voltage low-current
and low-capacitance nature lent itself to functioning also at higher
frequencies than those of typical video circuits.

Next I'll look into TV distribution amps. I remember that transistors
in those were designed to linearly pump a lot of different signals up
to UHF, and that they tended to run hot - and 24/7.