The space requirement and index fragmentation issue is nearly the same no matter what kind of relational database you use. Math is math.
Just the other day I delivered significant performance gains to a client by converting ~150 million UUIDv4 PKs to good old BIGINT. They were using a fairly recent version of MariaDB.
If they can live with making keys only in one place, then sure, this can work. If however they need something that is very highly likely unique, across machines, without the need to sync, then using a big integer is no good.
if they can live with MariaDB, OK, but I wouldn't choose that in the first place these days. Likely Postgres will also perform better in most scenarios.
I think the author means all dbs that fit a single server. Because in distributed dbs you often want to spread the load evenly over multiple servers.