I have met my very best friend in an FFXI exp party (we've been playing together for seven years now. He's the person I've had by my side the longest in my life, save my mother maybe), so I very well get your nostalgia. The story was great, the content was vast and accessible, the houses were free...
However, you have to understand, the gaming community has moved onto a new generation. A generation of "speed players"; people who study this evolution make phone games responsible of this. While phones have approached a LOT more people to gaming (remember when we were "losers" for wasting time on videogames? Now we're the cool stuff), it has also made people used to quicker games, that take less time to complete and entertain.
To appeal to this new generation, old games such as FFXI had to adapt. It went through many severe changes from how it used to be, to the point that some of the oldest players got overwhelmed and left, not recognizing the game they had been playing anymore. Many of us are fond of the memories of meeting new people and establish meaningful bonds with them.
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We were people with a lot more time in our hands. It was always common to find people willing to just approach the random newbie to show them the ropes;
Doing so in FFXI almost always inevitably lead to dreadful results that I well remember...
Assistance from other players in getting a sense of the game was replaced with Help windows in FFXIV, and as many others, it is a sign of a change in the community. A change towards individual gaming. Surely you do notice even linkshells have been turned into something completely optional, and that having so many and with so many people often breaks the closeness among the members, leading to hours of awkward silence on most of your LS channels.
And then, there were EXP parties. They could literally make or break your day, depending on the people you found there. With XIV's system, it is easy to replace unwanted fellows, but in FFXI? If your healer was an ass, you were more than likely forced to chew on your liver and stick with them, because chances are they were the only ones around. To find tanks and healers was very difficult, and some parties had to disband just because one of them had to go have dinner IRL.
In XIV you hear complaints for hours-long queues. In FFXI, it could take days. That is another sign of a drastic change in the MMORPG community.
At the first times, I think it was uh... 2008, maybe? Not sure.. SE introduced Level Sync to try and ease that. And for a while, it did work well.
But alas, it was only a temporary bandaid.
(Sorry, ran out of cool pictures from here)
Not only EXP parties take TOO long to form now, even Abyssea itself is now considered a "waste of time". So SE added Trusts, NPC party members to do your bidding with enhanced AI. They doubled exp from monsters, they made EXP chains bigger and gave people a "challenge log" of sort (it's called Records of Eminence, and it's not even weekly. You can repeat the challenges for as many times as you want), plus so many other buffs to make EXP easier to get: Fields of Valor, Grounds of Valor, Campaign Battles, unlimited EXP rings...
The result: you have your solo EXP party, with your own tank, healer, buffers, and DDs. I still play it so I know, last week I got from 18 Ranger to lv50 in a matter of four hours, all by myself.
It backlashes on making friends in the game, I realize that and I'm as sad as you are, but we have to accept that gaming is evolving in this direction. FATE parties and DF parties are today's version of FFXI's parties in outside areas or dungeons. I'm personally a little disappointed at the cross-server access of DF parties, as I'd like to get to know people on my server and make actual friends, but I realize that without it, we'd struggle to even find people for some content. FATE parties on the other hand, let you meet people specifically of your server, but they have no real mechanics, it's all whack and run, and once you're done, poof, you can leave without so much as a 'bye'. So you can see both have their cons, and neither will ever be what an EXP party was. But alas, it's what the playerbase needs. The newer generation just "has no time", you see? Games that take days to achieve even the smallest thing just do not sell anymore if not to a minority of nostalgic players like you and I, and we'll never provide enough money to gaming houses for them to put us on priority.
Last and not least, doing what you ask would require a great overhaul of the battle system in the open world, from their AI and levels (you can solo any monster at your level, even chocobo companions are redundant), to their aggro and reset ranges, to the exp they provide, not to mention the fact that they link in greater numbers depending on your party size, no matter of how clear your pull is.
With all this being said (I'm not trying to be pedant, just sharing my thoughts because just like you, I have been looking into this and these are my conclusions), as people said, no one stops you from forming a party with friends and 'fool around' for exp.