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I am pretty sure most of these vendors would offer strict guidance to not do that.Then you'd be wrong. Running Postgres or MySQL on the same host where Apache is running is an extremely common scenario for sites starting out. They run together on 512 MB instances just fine. And on an SSD, that can often handle a surprising amount of traffic.
As popularity grows, the next step is to separate out the database on its own server, but mostly as a side effect of the fact that you now need multiple web servers, but still a single source of truth for data. Databases are lighter-weight than you seem to think.