On the one hand, yes, you could use a general purpose string database to count/move integers, up to a certain scale. But a specialized integer database like TigerBeetle can take you further. It's the same reason, that yes, you could use Postgres as object storage or as queue, or you could use S3 and Kafka and get separation of concerns in your architecture.
I did a talk diving into all this recently, looking at the power law, OLTP contention, and how this interacts with Amdahl's Law and Postgres and TigerBeetle: https://www.youtube.com/watch?v=yKgfk8lTQuE
But this pattern is not required by PostgreSQL, it's possible to run arbitrarily complex transactions all on server side using more complex query patterns and/or stored procedures. In this case the locking time will be mainly determined by time-to-durability. Which, depending on infrastructure specifics, might be one or two orders of magnitude faster. Or in case of fast networks and slow disks, it might not have a huge effect.
One can also use batching in PostgreSQL to update the resource multiple times for each durability cycle. This will require some extra care from application writer to avoid getting totally bogged down by deadlocks/serializability conflicts.
What will absolutely kill you on PostgreSQL is high contention and repeatable read and higher isolation levels. PostgreSQL handles update conflicts with optimistic concurrency control, and high contention totally invalidates all of that optimism. So you need to be clever enough to achieve necessary correctness guarantees with read committed and the funky semantics it has for update visibility. Or use some external locking to get rid of contention in the database. The option for pessimistic locking would be very helpful for these workloads.
What would also help is a different kind of optimism, that would remove durability requirement from lock hold time, which would then result in readers having to wait for durability. Postgres can do tens of thousands of contended updates per second with this model. See the Eventual Durability paper for details.