I prefer leagues that move at a slower pace and there isn't a rush between seasons... I don't mind it taking a week or even two between the draft finishing and the league filing.
In fact, the "timeliness clauses" were the only reason I didn't join the NWP right out of the gate. And after the 1st couple of seasons I asked to be added to the waitlist instead of taking an open team, and then skipped the first expansion, all because I didn't like the thought of having to rush to get my team in. I don't always have access and am using my phone frequently. So, I'm often caught up on sitemails to me but don't always respond, Am occasionally several rounds behind in a draft as I haven't had a chance to research (let alone submit a proxy), rarely set my lineups or rotations before a league starts, and often am one of the last ones to enter their team. It's just that most of those things are not easy to do on ones phone and I prefer to do it right than to give a half effort; and thus will wait.
All that said, why try to implement something across all leagues. That's the beauty of the market, variety and choice is all around you. There are several leagues that are quite snappy with league rules about timeliness and then there are several others that encourage a more laid back approach. I prefer the latter, but will join the former for the company (as long as I don't have too many of those types of leagues already). I would likely quit most of my leagues if they began to implement such rules as I would not be able to comply and the penalties would frustrate me as I would feel like I was being singled out for something outside of my control. This is why the ability to participate in a variety of league types is nice as I can move at a generally slower pace for most of my leagues while one or two move more abruptly; allowing me the time to try to keep up with those without feeling pressure or stress from my other leagues.
I'd be more inclined to submit a GC and would play in a league like that, but not over this issue...