Some basic math.
If you play 18 holes in 3:45, that's 225 minutes, or 12.5 minutes per hole. So after an hour, you're putting on the fifth green when the single in your example catches up to you.
The single has played nearly five holes in half an hour, so a little more than six minutes per hole. His total round time would normally be less than two hours. (Given my own play as a single, and in some average foursomes, I don't either of these figures are wrong. In fact, they seem pretty dead on.)
But, the problem is this: you're justifying nearly doubling the amount of time it takes this single to play 18 holes (30 minutes to the fifth hole, and 2:43 to play the last 13, making their round take 75% longer) just so that you don't add a few minutes (and a few %) to the amount of time it takes you to play?
In carts, there's no reason letting people through adds a lot of time to your round. I'll invite a single to tee off with us, let him drive ahead while we hit the head or something, and by the time we're done he's gone and out of the way. Or we drive up with him, watch him finish the hole while we re-apply sunscreen, and again, he's done by the time we're done.
Put another way: if it only takes the guy six minutes to play an entire hole, you could sit there and let him play the entire hole you're on FOUR TIMES and still add only 24 minutes to your round time. Or let four singles play through - each waiting until the previous single played the entire hole before teeing off - and still only add 24 minutes (10% or so) to your round's time.
The math doesn't add up. Letting people play through like that should not add 30+ minutes to your time. I get that you're fast. You say you regularly let people through.
Your bizarre example didn't help you.
Whatever. Let's say we've just finished a hole and decide to let a single through. We follow the USGA's advice and wait on the next tee to let dude play through. We finish the hole and drive away to the next tee box where we hit our shot and wait for him. He has to hit his approach, putt out, get to the tee box, and hit his shot. We all drive to our balls where we let him hit and then wait on him to move on before we hit.
You think that he plays his approach, putts out, hits his tee shot (we're waiting on the tee for him), then after waiting for him to hit again and putt out again that only six additional minutes has elapsed? While we're waiting, he's played three (we'll add the time we wait on the box for him when we could be driving to our balls) full shots and putted out on two greens.....in six minutes?
Hey, if you're that fast, you can play through us anytime.