I have a couple of Hickok tube testers that have this function. For the most part, I have always ignored it when testing tubes and sticking with the pretty standard emissions and shorts tests. Lately, I have been studying the concept from a great old Electronics textbook, and it seems like it would be rather important. At least you are a person having concerns of picking the best possible tube for a special application out of a number of the same stock.

I think old radios and TVs have enough tolerance in their circuits that if a tube is clean of shorts, has no gas, and bears good emission than the work of the circuit will be done with no noticeable effect to the user. Am I right? Figured I would get lots of good insight here.

I have the Hickok 532 with the laboratory meter pack (6 meters). I rarely see it as a audiophile keeps it at his house to keep a steady supply of 12AT7 and 6AS7 tubes for his fire breathers. They are sensitive to transconductance tests.
Most of what I see affecting TV's and the more docile audio gear is grid leakage (6AU6, 12AU7 especially) and shorts. The B&K tube testers have good shorts and leakage tests. My Hickok will miss a leaky tube once and a while (don't flame me Hickok lovers) but when the B&K says leaky or shorted, you can count on it!

I have been repairing stuff for several decades and have used both transconductance and emission testers. Frankly, for me at least, the transconductance units aren't worth it. A tube isn't likely to change its gain when its parts are of a definite size and spacing. These testers are best for building tubes, or matching tubes from different manufacturers, in my opinion.

Every bad tube I have found tested bad on an emission tester.

I don't want to start any flames; these are my opinions based on lots of experience, and each person is an individual.

Haven't thought about TV apps in particular, but it seems to me transconductance might be more critical for high gain stages like the typical luminance output stage in tube color sets. I know different video output tubes that all tested OK for emissions made noticeable differences in video drive in the Magnavox I had, so might be the difference was transconductance.

Every bad tube I have found tested bad on an emission tester. I don't want to start any flames; these are my opinions based on lots of experience, and each person is an individual.

Shouldn't be any flames here. This is what I asked for; first hand information and opinions. I must add or say to both posts that it in my opinion is a given that emissions tests are going to be the number 1 issue with tubes. There is however two entirely electronic conditions that exist here, right down to the math. It is defined as the ratio of small change of plate current to a small change in grid voltage. The formula is Gm (sub m meaning mutual conductance) = the change in plate current divided by the change in grid voltage and is expressed in micromhos.

So this is certainly not possible without decent emission. In old_TV_nut's Magnavox I wonder myself if the difference was mutual conductance or simply different emissions measurements all measuring "OK" for that circuit.

One final (?) comment: if a circuit is properly designed, and calls for a particular component in the parts list, it should work properly with any component meeting those specifications. So tube selection shouldn't be necessary.

Having said that, the pressures of economics combined with the frequent incompetence of some engineers probably result in some marginal designs that won't work with the full spectrum of components. Worst case analysis was seldom used in commercial practice.

So measuring everything you can measure on a component can be useful, although one never knows what limits to use.