No to tube coolers and dampers.
No point. IMHO.
I am an Analog Tube Bot.
Opinions & experiences with tube coolers
Over the years, I have used products from Mapleshade Audio and other sources for conducting heat away from the tube envelope. Their full-length brass body placed over the tube and then adjusted, claims to have damped vibration as well as cool the tube surface directly. Pearl tube coolers are inexpensive, and I wonder if they do any sort of shielding as well. Taking unneeded heat away from the tube makes good sense to me, but does it provide other benefits?