The use would be disparate to carriers, which are mobile bases of operation.
I think the answer to this question might be easier once we know more about what Odyssey is going to offer (after all, this could very well be the carriers for surface content in many ways).
But, ignoring that, don't underestimate the desire for a "home". An actual home that's yours, complete with your chosen vistas, interior options and local to the system you feel most comfortable in. I'd suggest basic benefits such as additional module storage, commodity storage, shipyard, outfitting (perhaps outfitting could be much easier/cheaper to stock on inhabited planets, too, due to lower logistical costs), apex, depot. Perhaps more, linked to whatever new stuff we get to do on the planet surface in Odyssey. An additional perk can be reduced or no costs for some stuff. And your friends can use that too.
Ultimately, carriers only serve one purpose yet they're used for more than that. So even just "a place to keep my stuff" is enough of a reason.
Single cost, plus cost of additional services and "rooms", no upkeep but if you want to move house, there's a big cost involved. And it takes a week.
Just spitting out ideas. But I'd want one if they existed and more so if there's enough Odyssey content on surfaces to make having that base worth while. To a certain extent, this all depends a lot on that.
Thing is, to me, all that is already in the game in the shape of my carrier - it's my home, it's where I store all my stuff (including all sorts of cargo), it provides a vista (ever-changing, unlike a fixed base on a barren planet), I can make it a shop-front if I want to. The bit that isn't covered currently is indoor space, and that could in theory become part of a FC if and when ship interiors get added (though we don't even get a lousy bridge view while all ships have at least a cockpit, so I'm not overly hopeful on this).
A base would need to offer me unique gameplay that other assets in the game don't offer.
Let's just run with the idea of a custom mission board. I personally would really like one, but even those are much more suited to FC's - why? Because presumably NPCs can't interact with your mission board (just like they can't with your FC in general), so it'd likely be limited to other players, and it's just easier to bring the mission board to players (in the form of a mobile base) as opposed to the other way around. Imagine having a base in some backwater system with no traffic - what use is a mission board there?
And it's unlikely that I will run my own missions as I want to be surprised by the game in terms of what tasks it wants me to perform. YMMV of course.
It does remind me a lot about the Hearthfire DLC of Skyrim, i.e. the family home content. I own it only because it was part of the Legendary Edition, and I wouldn't have bought it on its own, because that's basically playing The Sims in a game that's not really made for that (you may disagree on this of course which is fine).
I still fail to see what bases could add in terms of engaging gameplay that FCs don't already provide, besides it being fixed to a given location (which is a downgrade in my view and I wouldn't bother unless I was utterly bored with the rest of the game, and I certainly wouldn't pay for it if it was a standalone DLC).
EDIT - if bases would allow for the creation of self-sufficient mini-bubbles, now that could possibly win me over if I were interested in creating a little hippy community with other players in the middle of nowhere.