There is only one database for everything in the business? Of course it doesn't scale. The problem you describe stems from solving every business request by adding yet another table to 'the' database.
It's a monolithic solution. It doesn't matter if you use database features or not. There is no difference between a mess of stored procedures and a mess of business logic classes. It's still a mess.
Web servers usually scale better than (traditional) databases, so it makes sense to not offload computation to the database, even if it means that there's an overhead.
That's very situational. Read scaling a database is easy. Write scaling a database is harder and doing computational logic while write scaling a database is harder still. Computational is still a very broad word though and the intensity of those computations is a huge defining factor.
The problem boils down to the "the database" idea described earlier. There are very, very few normalized datasets that I've ever seen that have write scaling concerns on more than 1 or two tables.
Move those to a separate datastore that is built for it and you've largely solved your problem. Postgres can even connect to outside datastores to run queries against them for sake of reporting.
There is only one database for everything in the business? Of course it doesn't scale. The problem you describe stems from solving every business request by adding yet another table to 'the' database.
It's a monolithic solution. It doesn't matter if you use database features or not. There is no difference between a mess of stored procedures and a mess of business logic classes. It's still a mess.