A lot do. Or rather they care about the proverbial carrot. Take away mounts from the extreme primals and I guarantee each and every single one will be dead content within a month; two tops. How many people complain about running the same two dungeons? If they could hit 2000 Scripture in a week and gear up their main job. How often do you think they'll keep running those same dungeons? I barely run them even with the tomestone restrictions. It's simple human nature. Most people won't do something unless they are in some way benefited. At least not consistently. No matter how nice and helpful someone may be, eventually they'll get tired. And this doesn't even take into consideration crafted gear becomes completely worthless. Who's going to buy gear of the market board for thousands when they can spam Gubal Hard ten times? What about Alex Normal. Clear it once and just spam dungeons for Scriptures. Even if you bump everything up to 260, people will then farm whatever happens to be fastest.
None of this insinuates players only play for gear. It merely posits most won't run content 20-30-50 times for no reason other than "the dungeon looks pretty."
A perfect example are the 24 man raids. Crystal Tower was dead content until the Anima forced us all back into it. How many people would run Void Ark/Weeping/Dun Scaith if they could get everything they wanted in a couple weeks-- less if they're willing to farm?
Very few people abruptly change jobs during progression, especially as statics often try to build around what you're previously selected. How often does say, a Dragoon decide, "I want to go Bard" three weeks into Savage? A good number of statics would flatout kick you if you insist because they'll now have three ranged and you already agreed to play a melee. Even were that scenario to occur, it's not like you cannot obtain enough gear to make it work. A9/A10 were easily pug-able this tier. If you wanted to swap jobs, get some accessories and maybe something on your left side. If that still isn't enough, sorry but... plan ahead next time. You don't go into Savage level content thinking "I'll play and gear whatever. Everyone'll be okay with that!"
What you're asking is to design a system around people being indecisive. You have four weeks before you can even buy something with pages; six if it's anything except accessories. If you can't commit to one job by that point, it isn't the game's fault. Regardless, this still brings us back to if you can farm everything from the onset, you take away any incentive to keep playing later on. And as I already mentioned above, unlocking tomestones destroys most alternative gearing methods.
Let's break it down.
3.4 released
ilvl 250 Proto-Alexandrian
ilvl 250 Crafted
ilvl 255 Sophic weapons
ilvl 260 Shire
ilvl 270 Alexandrian
ilvl 270 Augmented Shire
3.5 released
ilvl 260 Diabolic
ilvl 265 Zurvanite weapons
Shillings were added to upgrade Shire weekly
ilvl 270 Proto-Ultima accessories
From this list, we can immediately cross out all 250 gear and the 260 Diabolic. It's rendered instantly obsolete since why farm inferior gear with RNG when you can just spam faceroll dungeons? If the loot restrictions on Alex normal are also removed, well, you don't need Sophic weapons. People have no reason to run A9-11N more than once save occasional fun since you get nothing out of it; run A12N seven times per job and that's irrelevant next. By the time 3.5 drops, people literally only need to run Dun Scaith to upgrade their Shire. And if it lacks restrictions too, they can spam it. Even if you aren't hardcore, it doesn't take long nor do you need get everything. What about Solm Al and Baelsar's Wall? Four months later, even snail pace players will likely have farmed all they want scripture wise. Now you have two dungeons that will only be popular for a week or two as there's no reason to run them.
Basically, it invalidates a large amount of content. These restrictions are meant to keep people subbed. Some, like Momo will wait out the restrictions and return when they can gear however they please. Most won't. They'll play whenever the new patch launches and whether it takes two weeks or two month, be set gear wise and have no incentive to run any content. Raiders will be bis within the first month and likely unsub by 3.5 once they've exhausted speed killing and casual players will struggle dealing with slow queues in content no longer needed. I didn't even mention dungeon and diadem gear. It's pretty much DOA. Unfortunately, there has to be some form of limitation on progression in a sub based game. If not tomestones then RNG or some other potentially annoying restriction. Being able to get everything you want quickly removes player incentive to continuously play. Some games limit progression with week restrictions while others gate through immensely long grinds (Black Desert and Blade & Soul). They all serve the same purpose; keeping the majority of players subbed. I won't say FFXIV can't improve. It's certainly far from perfect, but there will always been a limit.