I think you’re imagining that moving business logic into stored procedures will overload the database server sooner than having that in application code. I have never seen that. Instead you get fewer simultaneous connections and less data passed back and forth. Querying a compiled view or stored proc will often use fewer resources than parsing, planning, and optimizing SQL sent from application code. And the RDBMS can make better use of caching with business logic in the database.
Scaling and replication may present complications with any architecture, but those aren’t good reasons in my opinion to not put business logic into the RDBMS. Real enterprise-scale databases tend to do that and they actually have scaling and replication issues, not just “may happen someday” issues.