One of the reasons I like the Black Hack-based games so much is the leveling mechanics, where there’s a chance for every stat to increase, and in some games certain attributes can even increase twice. I’m generally not a big fan of class and level systems but I can tell you from experience players love leveling in TBH specifically because of this attribute rolling.
In my current Rad-Hack game, which in our case is one part Gamma World and one part Fury Road, the PCs hit level 3 last weekend. The mutant fungus PC has gone from an INT of 2 at level 1, to 4 at level 3. He went from just being able to say his name in different ways to mean slightly different things, to now learning his friends’ names and even stringing together short sentences. He also tamed a giant radioactive snail that now travels with the party, but that’s a story for another day.
Bottom line, in my experience, players really like the chance to increase stats when they level. Do it, @LaramieWall!