Postgres is happier with sequence ID's, but keeping Postgres happy isn't the only design goal. It does well enough for all practical purposes if you need randomness.
It literally is the one thing in the entire stack that must always be happy. Every stateful service likely depends on it. Sad DBs means higher latency for everyone, and grumpy DBREs getting paged.
There are some pragmatic differences I've found, though - generally, DBAs are less focused on things like IaC (though I know at least one who does), SLIs/SLOs, CI/CD, and the other things often associated with SRE. So DBRE is SRE + DBA, or a DB-focused SRE, if you'd rather.
I don’t think people grasp how far a single RDBMS server can take you. Hundreds of thousands of queries per second are well in reach of a well-configured MySQL or Postgres instance on modern hardware. This also has the terrific benefit of making reasoning about state and transactions much, much simpler.
Re: last bit of performance, it’s more than that. If you’re using Aurora, where you pay for every disk op, using UUIDv4 as PK in Postgres will approximately 7x your IOPS for SELECTs using them, and massively (I can’t quantify it on a general basis; it depends on the rest of the table, and your workload split) increase them for writes. That’s not free. On RDS, where you pay for disk performance upfront, you’re cutting into your available performance.
About the only place it effectively doesn’t matter except at insane scale is on native NVMe drives. If you saturate IOPS for one of those without first saturating the NIC, I would love to see your schema and queries.
See Snowflake IDs for a scheme that gives you the benefit of random UUIDs but are strictly increasing. Which is really UUIDv7 but fits in your bigint column. No entropy required.