You still have to wait for the green to clear before advancing to the lay up. If you are waiting for any reason, that wait is typically compounding behind you.
So instead of: hit -> walk -> hit -> walk -> hit -> walk -> green (seven stages), you have: hit -> walk -> hit -> wait -> walk -> hit -> walk -> green (eight stages).
But if you're waiting for the green, then that wait just comes before the hit, so it's still eight stages. If you're 250 yards away from the green, you can either hit one shot or two shots (don't lay up vs lay up). If the group ahead is still on the green, then if you hit one shot, you have wait, hit, walk, green. If you hit two shots, you have hit, wait, walk, hit, walk, green. So yes it's an extra step in there, but that's really because one 250 yard walk has turned into one 150 yard walk and one 100 yard walk. Those take the same amount of time don't they?
Having said that, I thought about this a bit more and I think the issue is actually mixing and matching going for it and not among different groups. I went through the bottleneck math for alternating going for it and not.
If everyone lays up:
Group 1 plays tee shots (3) walks (3) hits second shots (3) walks (2) hits third shots (3) walks (2) green (4) = 20 minutes
Group 2 has to wait 9 minutes for this group to clear before they hit their tee shots. So they wait/finish prior hole (9) play tee shots (3) walk (3) hit 2nd shots (3) walk (2) hit third shots (3) walk (2) green (4), so they finish the hole at 29 minutes after group 1 tees off and I think that's consistently how long the field should take. And the 9 minute wait matches the prior hole's approach shots (3) walk (2) and green (4).
Alternatively, if all players go for it in 2, I think it would look like:
Group 1 plays tee shots (3) walks (3) hits second shots (3) walks (4 - since they have to walk the same distance as in the prior example) green (4), so 17 minutes and now group 2 again has to wait 9 minutes while they clear the prior hole. Then they tee shots (3) walk (3) wait (2 - since group 1 takes 8 minutes to finish the hole after clearing the tee shot area and it only takes 6 minutes to hit tee shots and walk) second shots (3) walk (4) green (4). That's 19 minutes total. Group 3 are going to wait 2 minutes on the tee, then 2 minutes in the fairway as well, so every group is going to have to wait an additional 2 minutes over the previous one, so 11 minute gate time (I think).
If you have a mix of going for it and not, let's first look at it as group 1 lays up and group 2 goes for it. Now:
Group 1 tee shots (3) walk (3) second shots (3) walk (2) third shots (3) walk (2) green (4)
Group 2 finishes prior hole in 9 minutes then tee shots (3) walk (3) - that's 15 minutes total, so they have to wait 5 minutes for the green to clear. Wait (5) second shots (3) walk (4) green (4). 31 minutes since group 1 started. Now group 3 lays up, so they have to wait 14 minutes till they can tee off, They have a five minute wait on the tee, so wait (5) tee shots (3) walk (3) second shots (3) walk (2) third shots (3) walk (2) green (4) so that's 25 minutes for them on this hole.
Group 4 is also going for it. They have to wait 5 minutes on the tee also (group ahead 5 + 3 + 3 + 3 - 9), but that should be it because group 3 can hit their lay ups without further waiting (group 2 being on the green at this point). Now group 4 waits (5) tee shots (3) walks (3), so that's 6 minutes after group 3 cleared the driving area. But group 3 are going to take 14 minutes to finish the hole after clearing the driving area, so group 4 after waits (5) tee shots (3) walks (3) wait (
second shots (3) walk (4) green (4).
Group 5 gets to the tee 9 minutes after group 4 did. But they have to wait 5 + 3 + 3 + 8 + 3 - 9 minutes which is 13 minutes. Things are getting ugly.