My point is that it should not even be a question about what use as a weight.
A physicist is someone who does new science. Someone who works to add scientific knowledge to humanities understanding of the physical world.
Popularity, TV appearances, Pop. science books, etc. may make one a face of science or allow one to educate people about science, but those are separate tasks. Doing those things does not make one a physicist.
Sure, someone can be both a good physicist and a good educator. However, just as being a great scientist does not make one a great educator, being a public educator should not be used as a measure of one's contribution to physics.
So, yeah sure. The answer will depend on what we use as a measure of a good physicist. However, only one of the measures you gave is a good measure.