I rather have data separated from operations done on data. I am very happy since I don't have to deal anymore with stored procedures.
For many things, having an “application server” running code that is merely chaining SQL queries (often hiding them with an ORM and performing way too much queries, destroying performance in the process) is not a particularly good idea… The main reason we do it is because we can have a proper debugger, write unit tests, have an IDE, etc. but there's no fundamental why stored procedures could not give the same developer experience, except that RDBMS vendors don't give a sh*t.
However, one other concern is that scaling out databases is much harder than scaling out stateless processing layers, and therefore at scale there's a huge benefit to separating as much out of the storage layer as possible.
So in many cases it is preferrable to extract as much as possible any computational etc parts of an application from DBMS to separate stateless components that can then be scaled/updated/maintained/etc independently.
Some sort of check pointing is inevitable for recoverable state-less systems (that naturally react to a stream of data/queries) and that ultimately is delegated to either a streaming/messaging (e.g. kafka) or a database (of some sort).
Components of an application hosted in a RDBMS are tables, indexes, views, and code. The code is stateless — they’re just functions. Application state is in tables. Replication is supposed to handle your more hairy operational concerns. What’s the problem?
Replication is slow, and requires each node to have lot of resources, and generally prefers nodes to be realtively homogenous. But for non-trivial applications replicating the whole application (or some shard of it) to all nodes is simply impractical, and it is useful to be able to scale and adjust different parts of system independently.
For example on AWS Lambda you can scale out up to 1000 new instances per 10 seconds (and scale in at similar rate). Can you imagine any DMBS replication working very effectively at such circumstances?