HS has max cap at around 75k.
Let's say after RoR settles down it averages: 120 ppl per BG, 120 BGs and 50 back-ups.
That's about 14k guests guaranteed rides, and 6k who have a decent shot.
1/3 of max cap arrives, so 25k ppl out of 75k possible.
There are 20k slots to give 25k ppl, so a 4 out of 5 chance to succeed.
Let's take that to 4 time windows-
Park open: 25k guests there, 5k get a BG. 1 in 5 chance to succeed.
12:30p: 45k guests minus 5k with BGs, so 40k and 5k get BG#2. 1 in 8 chance.
3:30p: 55k guests minus 10k with BGs, so 45k and 5k get BG#3. 1 in 9 chance.
5:30p: 45k guests minus 15k with BGs, so 30k and 5k get BG#4. 1 in 6 chance.
Attending all 4 windows, you now only have a 3 out 5 chance to succeed. For every window you missed, your chances go down further. For guests who are trying during the 2 midday windows, they'll likely have to show up to HS 3 or 4 days before success at BG.
We also rode on MFSR (twice), ToT, RnR, AS2, and Star Tours, we saw some Storm Troopers walk around, we drank blue milk, I got selected to be an extra at the Indiana Jones show, we got a drink at Oga's Cantina, we saw fireworks, we saw Fantasmic. We didn't get to ride SDD or TSM, my wife and daughter didn't get to enjoy a vegan sundae/milkshake at Sci-Fi Diner or 50's Prime Time Cafe, it took us nearly two hours in the single rider line at RnR since I couldn't get a FP for it. Removing RotR from that whole equation still meant we had a fun day.
That sounds like fun on Day 1. But if you really wanted to try RoR, Day 2 will not be as fun as you did most of what you wanted already. By Day 3 and 4, you'll be upset and will try to see what Guests Relations can do to help only to notice that line has grown to a 2 hour wait with all the other unsuccessful guests.
I'm ballparking here, but however I play this out in my head, staggering just seems to be full of more issues than the current method.
A lottery may work. I'm not sure how Japan goes about it, but I'd imagine potentially they can keep track of how successful/unsuccessful a guest has been at previous attempts and take that into consideration when determining a fate.