Hello, I'm replying on behalf of the Silferian Empire, and the following (non-exhaustive) list of AFs with a brief rundown of their purpose:
-Conflagration (Public Darkroom/Facilities, Private Build)
-SilferiaHQ (Shared Kingdom Facility, Private Build)
-KaiserreichAF (Faction Facilities, Farm, Private Build, etc.)
-KRDarkroom (Warp Teleport to Darkroom, Private Build)
-BelloqInc (Private Build, formerly Looting)
-Crypt (Faction Facilities/Farms)
-Prussia (Faction Facilities, Private Build)
-Nilfgaard (Faction Facilities/Housing)
-Inolaath (Vault, Faction Facilities)
-Parallax (Darkroom)
-SolverisDR (Darkroom)
Granted, the majority of these are in Essalonia, with only KRDarkroom, KaiserreichAF, BelloqInc, Nilfgaard, Inolaath, and SolverisDR having land in Essa, and all but SolverisDR having less than 60 chunks (and for most, less than 30 chunks).
From most of what I've seen, most people use AFs to get work around the clunky, unintuitive, poorly put together perms system that's a jury-rigged holdover from the days of Cayorion back in 2011. What we need is the ability to dictate exactly what someone can or cannot do within a bounded region within our factions.
They also use AFs to create shops, markets, libraries and museums, darkrooms, grinders, public farms, etc - all well implemented in ways they could never pull off with the current permissions system in their own factions - unless of course you go full Salemslot and build your entire faction around that purpose, which most don't want to do.
What do you use them for that you couldn't in your main faction? / Why are they important to you?
Permissions Granularity:
Alt Factions, and generally factions that are detached from the main faction, are immensely useful in providing faction leaders with permissions granularity and functionality that we've been told would take tons of time and effort for the Tech Dept. to give us within our own factions.
For example, I have an Asteria-style plot town I let my members build at, but I also have a more traditional city elsewhere. Let's say I want to grant a low ranking officer the ability to grant access to new members in the plot town, but I don't want them to be able to grant access to the town or faction facilities and stage a repeat of the Pettiget-Solveris Incident. Splitting off the Plot Town into an Alt Faction allows us to specifically grant access perms in a limited manner, without putting the parent faction at risk.
This extends to basically anything you want to have limited perms without granting full access to the chunk.
Player Freedom
I find this one extends less to me personally, but does affect some friends and other members. Being able to just have your personal build or vault or whatever in it's own AF is far more convenient and player friendly than forcing these players to be in a 1 man faction... and no, I disagree heavily with the sentiment that "Oh just create a Kingdom and then you can have all your 1 man facs in the Kingdom and with Kingdom Chat it's just the same thing - as a Kingdom Leader, it's in no way shape or form the "same thing" as being in the same faction as eachother, and it packs in a ton of extra added risk for no reason, particularly with Sieges.
NdFeB also sums this one up beautifully in his post.
Use as Warps and Facilities/Darkrooms:
As you can see in the list above, the majority of the AFs we have are facilities such as DRs, Farms, Grinders, etc. Facilities you may not want to have in your town, or that are limited by the current faction Flags system. Also, you can use AFs to allow you to create warps/tps to various facilities (such as my /tp krdarkroom) without having to use clunky portals that are hard for new players to understand. Also many of these facilities, such as Darkrooms, are critically important to the current economy, with no real strong replacement put forth by staff at this point.
Lastly what could be offered from massive to have their functionality replaced?
Permissions Granularity:
To provide additional permissions granularity would require a significant overhaul of how permissions and flags work within factions.
Some of the ideas below:
-Give us the ability to have a deny-override over any inherited perms on a specific entity, e.g. /f perm set <perm> <entity> deny <facname-optional>. This would override any and all inherited perms. (e.g. I have an ally who I don't want to be able to f home, he would not be able to f home if I denied him the perm).
-Replace the current /f access system with a system of leader/officer created regions, not unlike a WorldGuard Region, where we can dictate exactly what perms <entity> has. Also allow us to set flags within this region, e.g. I can set mobs to spawn in this small area underground but not above ground.
Player Freedom:
There's no suggestion unless you allow us to have AFs that are purchased through Regals instead of using an Alt, e.g. Warzones. However, given the extra staff work of keeping up with disbands this would create, it's far from an appealing solution.
Use as Warps and Facilities/Darkrooms:
Like before, there's not really many way to replace these facilities, particularly darkrooms (requiring the monster flag). One of the suggested things I've seen is allowing us to create custom warps, but that's been shot down as well.
Is removing AFs Necessary?
Adding this here. Most of the "alternative" suggestions appear to require a significant amount of Tech Work, among other things. From my perspective... the easiest and least effort solution for Massive is simply to leave AFs the way they are and reopen AF claiming on Essa. Keep Essa as the "AF world" and have AFs turned off in the other worlds, or maybe turn them on gradually as new worlds are released, keeping them off for the newest worlds.
What problem is actually being solved by the removal of AFs? No one's given a good reason for removing AFs that can't be mitigated with well-crafted rules (e.g. member limits, claim limits, etc) other than "it's P2W" - but I don't think that argument is strong enough to merit a complete game-change of how Massive operates. The majority of users have interacted with AFs in some way, shape, or form, most positively, such as /tp darkroom and /tp krdarkroom. AFs aren't just about private ownership - they're valuable tools, workarounds to an antiquated system, and an easy means to encourage community cooperation and interaction - without requiring a ton of costly tech work and changes to the server.