jostber,
I too run a Cornet 2 and a Clarinet and use dampening on all tubes. This is a tweak that does seem to have merit and I can't theorize how it could be detrimental as long as you're aware of the basic thermal requirements of any vacuum tube.
For the signal tubes, I use two or three turns of teflon tape, wrapped around the upper portion of freshly cleaned pins and roll a snugly fitted teflon "O" ring down the glass. The rectifier tubes get the same treatment with the addition of a few runs of teflon around the junction of the plastic base and the glass envelope.
If properly designed, (for example, tuning for specific resonances) I'm sure that the various commercial products may, in some small way, be more effective. But ... for 10% of the cost of ONE commercial tube dampener you can get 95% (my personal, perceived, undocumented estimate) of the positive attributes of dampening for ALL of your tubes... well ... it's an inexpensive way to experiment.