And I'm not sure how licensure comes into this. Neither the 1994 FAWB nor the proposal you linked license the possession of "tactical rifles." They ban them with grandfathering. And for what it's worth, I don't think licensure regimes necessarily are irrational.
I think in the 1980s an outright ban on tactical rifles could have worked. That's the context of the bill. Since then, the black rifle has become a de facto standard platform for hunting and sporting, the market has followed, also somehow a feral hog explosion, and so an outright ban would be very disruptive. My point is that bans aren't the only option, and, in 2020 (but not in the 1980s) the cost of a ban would outweigh the benefit.
I think reasonable people can have all sorts of opinions on what kind of regulations there should be around firearms, and my confidence in my own beliefs is not all that high. But I am fairly certain that thought-stopping appeals to the definitions in the FAWB (or, for that matter, to the Sturmgewehr) don't make good arguments, and can be quickly disposed of.
I don't think mandatory licensure of tactical rifles is an irrational idea at all.