What is appealing about living campaigns like PFS?
I won't say that organized play and more typical home-games are like apples and oranges, because they're not quite that different. Instead... let's go with apple juice and apple pie. They both come from roughly the same source, but some people love both, some only like one, and some don't like either. And that's fine. The important part is that they're distinct things and serve distinct roles. If you want a drink, you don't lament that the juice isn't pie. If you want a snack, you don't lament that the pie isn't juice.
I make this point because I commonly see people complain that they don't like PFS because they like xyz in their home game better. That's ignoring that they're very different things on the level of fundamental structure and have different purposes. If you want a long-term immersive RP experience, you don't go to a public PFS game (for the sake of argument, I'm ignoring those home groups that chain-run PFS content with the same players and characters to make it into a pseudo-campaign as those are, if not rare, at least not typical).
PFS games definitely don't offer quite the same things as home games. They aren't meant to. You have the much-loved/much-hated magic-item-supermarket. You have the inconsistent cast. You have standalone episode stories that only rarely connect with sequels. You can also have issues related to the other players you wouldn't have in a home game (not after you boot them, at least).
What does it offer instead, though? Well, let me take my local PFS for an example. There are 2-3 games happening 5 days a week at a variety of locations around town. If I want to run a game one week, it's pretty simple for me to to do so. If I want to play two weeks after, I can also pull that off. If I want to take a month off? Also easy. The schedule fits with inconsistent life schedules, which a lot of people have. If all of that fails, i can probably get together an online group any given night of the week and have at it for a session or two. Contrast that with a typical "every Tuesday night" home game.
The materials also tend to be of pretty good quality. I ran PFS #7-10 a couple of weekends ago, and it's a very well put together scenario that isn't linear and allows for the kind of heist-planning RP that you don't often get in Pathfinder in general. Later season scenarios tend to be well written and offer multiple alternatives to problems, from diplomacy to skill checks to just outside-the-box thinking. Earlier seasons had more issues, and there are a few scenarios where the author needs a swift kick in the shins - but most are better than that.
The drop-in nature of the game also lets you do a lot of mechanical stuff in the game you might otherwise not get to do. Want to try out a new class? There are lots of ways to do that and not have to develop a big backstory and be committed to playing that character for months and months, even if you decide you don't like it. It's not uncommon to meet folks with 10+ PFS characters who have tried a whole lot of stuff.
In addition to the lack of long-term commitment, your achievements are also portable. You managed to defeat that dragon and took its hoard? That's on a sheet that you can take to another game and it will have happened for your player. Try moving the same PC between two or three home games and see how easy that is for comparison.
While characters change a lot, local groups tend to have a lot of core people that stick around. It makes it a bit of a social club where you can go in, meet a few new people, and reconnect with old acquaintances. As a warning, there are some areas where the local scene (either as a whole or particular pieces of it) is toxic and worth avoiding. It's unfortunate, though I've not had much of that issue in my area.
My personal experience these days is with PFS, but the 5e thing must be pretty good, too, since they always seem to have 2-3x as many tables as PFS at local events. Some of that might be that the local organizers are good people, but I haven't played any scenarios so I don't know what it's really like. I assume it's much the same, though.