This is an opinion. You think it's unfun and annoying. That doesn't mean everyone else does.
There have been instances of one sitting runs and divided runs that work out fine. That's what I've been trying to to tell you. But, again, you don't actually read what I write because it doesn't fit the way you want things to be. And are you sure this is an NA-exclusive thing? Any proof that this isn't also done on JP servers? Or EU servers?There's a reason why NA tend to do it all in one sitting, and that's due to those factors. Not everyone likes them, which is why pf and df exist. HoH removes that more or less entirely for the challenge floors, and previously potd kind of suffered because of it
Basically what you want is to be able to pug the higher floors at your leisure. Sorry, but that's not the way the content is designed. From the shenanigans I see happening on floors 21-30, I wouldn't want my floors 91-100 reliant on 3 other random people that use pomanders willy-nilly, or don't bother to use them when a situation is dire. Or get a party that's 4 DPS with no tank or healer. That's a recipe for disaster up on those floors.
To make them puggable, you would basically have to remove the challenge from them entirety: paper mobs that can be downed in 10 seconds with zero threatening mechanics to them, and each set of floors plus the boss takes 30 minutes or less. Which would defeat the entire purpose of those floors. They aren't made to be puggable in the sense of random matches parties. They're made for premades where communication is used and needed.
If you want to do them so badly, rise to the challenge. Plenty others have done it.
As for your IRL time constraints: I cleared PotD Floor 200 working a full-time job that never had the same schedule each week, and I very rarely had weekends off. I still made it work with friends a couple of hours each night for 3 to 4 nights until we cleared. It wasn't hard or stressful or annoying. Go with people you can trust and rely on, or start networking to find those types of people. You like to bring up FFXI, well networking and forming parties was core to that game. So do it in FFXIV as well. It's not difficult.