As somebody who likes stats and sandbox and all that himself - if done well it can add a more rounded feeling of progression and accomplishment in my eyes - uhm, no. Plain "no". By which I mean to say "Nope, not a good idea".
LRH was started as an AVN roughly 4 years ago which means the whole story, the whole progression, everything that is done here was made on that basis. You cannot just slap a new mechanic onto this, even if we all agreed that 'boxes would be more enjoyable, because it would basically mean the whole things need to restart. I mean, many story scenes could stay as themselves, but it would require a complete rethink of when or how those will be reached. It is not only adding the filler stuff, it is placing it, making a workable storyline if stats aren't met, account for different stats being reached at different levels, or similar. Unless you do it all linearily (Want to do X - do Y times of Z training now), in which case however it would not change the character of the game and just add the dreaded "needless filler".
"Stats and training" may be a good idea for other games, and it might have been a good idea for this ages ago - that can at least be debatable - but that ship has sailed, reached india, came back with tea, has been repurposed for coast guard services and later as a ferry so long ago, it is even debatable it is the same ship anymore.
Adding a completely new mechanic or idea to this now is just like going to some random non-incest game and suddenly asking to add a sister (never previously mentioned) because sisters are hot, or suddenly add BDSM to a vanilla game - it would be completely out of context, deter all but a very few even of those who like that content in general because here, for once, it just doesn't make sense.
Think of all the stories we hear from video games, movies, etc. where some exec suddenly got the idea "now X is popular, we must insert it into our game Y", even if "X" is a cover shooter mechanic and "Y" a pinball game, making really bad games. This idea with stats is just that. Except that sandboxes aren't even that much of a box office hit to begin with.
