For me at least, AO3 locking serves a few purposes:
First, it makes it ungooglable, and also really hard to automatically archive on sites like wayback or scrape onto sites like those for-pay fic apps that pop up once in awhile. So it does give some control over who sees your work.
Second, it makes it so that anybody who admits they saw it is also admitting they have an AO3 account. So they can't claim they were a pure innocent who knew nothing of fanfic until they stumbled on my work! If they already have an AO3 account they did not stumble, they sauntered vaguely downward a long time ago. Also sort of more conceptually, archive-locking feels like "I am posting this for the AO3 community to see" not "I am posting this so that as many people as possible will see", which can feel more comfortable if you're posting something that feels a bit risky.
Thirdly, if they have an AO3 account they're accountable to the TOS in a way anons aren't, in that if they break it, they can get banned. So archive-locking fic in theory means that people who have been banned can't see it (and also that if someone does something ban-worthy in the comments, I can report them and they won't be able to see it anymore.) Yes they can just sign up for another account but Abuse really tries to crack down on that. (And for a Mature or Explicit work, it means they have specifically set in their account settings that they want to see Mature and Explicit work, so they also can't claim that explicit work is being shoved in their face.)
Most of the fandoms I know that are heavily archive-locked are RPF fandoms where the people involved are known to be terminally on the internet; that way if the people involved read explicit AO3 fic about themselves it means they knew what they were getting into and made a clear-headed choice to read explicit AO3 fic about themselves.
Re: Thanks for bringing this up!
First, it makes it ungooglable, and also really hard to automatically archive on sites like wayback or scrape onto sites like those for-pay fic apps that pop up once in awhile. So it does give some control over who sees your work.
Second, it makes it so that anybody who admits they saw it is also admitting they have an AO3 account. So they can't claim they were a pure innocent who knew nothing of fanfic until they stumbled on my work! If they already have an AO3 account they did not stumble, they sauntered vaguely downward a long time ago. Also sort of more conceptually, archive-locking feels like "I am posting this for the AO3 community to see" not "I am posting this so that as many people as possible will see", which can feel more comfortable if you're posting something that feels a bit risky.
Thirdly, if they have an AO3 account they're accountable to the TOS in a way anons aren't, in that if they break it, they can get banned. So archive-locking fic in theory means that people who have been banned can't see it (and also that if someone does something ban-worthy in the comments, I can report them and they won't be able to see it anymore.) Yes they can just sign up for another account but Abuse really tries to crack down on that. (And for a Mature or Explicit work, it means they have specifically set in their account settings that they want to see Mature and Explicit work, so they also can't claim that explicit work is being shoved in their face.)
Most of the fandoms I know that are heavily archive-locked are RPF fandoms where the people involved are known to be terminally on the internet; that way if the people involved read explicit AO3 fic about themselves it means they knew what they were getting into and made a clear-headed choice to read explicit AO3 fic about themselves.