Full-frame is fine for someone like me, born in 1971 and accustomed to the format. Another five or ten years, you're going to have kids who are being born and will have never been exposed to 4:3 programming and keeping TNG framed as a 4:3 presentation only will make it look out of step with current programming.
Just like no one today enjoys movies made before 1950 or so because all of those movies are in a 4:3 or similar format.
But you have to admit, that those people are a fairly small group. Audiences are dying and being replaced by younger ones. Ten years from now, the likely available content of black & white material will be even smaller because you'll have fewer people who were ever exposed to the material to begin with.
So, you can either "future proof" shows like TNG or you consign them to ever shrinking audiences and the day will come when there will be no one watching. I'd rather there be folks watching TNG which has a 16:9 aspect ratio than no one watching TNG at all. YMMV.