Yes, there may be more galaxies than stars in our milky way. But almost all of them are extremely far away and we will never have a chance to interact, or even visit them. Worse, the rate they are moving away from our galaxy/local cluster is accelerating. We have a bit time to study those galaxies before they fade into the eternal redshift, but the real interesting stuff, what at least has a decent chance to matter beyond pure curiosity is what Gaia observes.
Until they are so far redshifted that they fade into background noise. And the expansion of the universe is accelerating. We have a bit time to watch this spectacle, but the fate seems it is just our local cluster that will matter, for most of the time while stars generate heat. That is why I am not so keen on emphasising the billions and billions of galaxies. It's only a nice good-bye firework.
Edit: I still think there are much more galaxies in our universe than stars in our milky way: The universe must be bigger than our observable part and there is no reason to believe that it is much different there (read less or no galaxies) than where we happen to be. So the "eternal redshift" already happened for many galaxies (from mutual perspective).
