PostgreSQL vs Sqlie - sure, no argument there, i am talking about a reasonably complex thing like PG/Oracle/MsSql.
Well, of course, it's easy to use what you already know as opposed to the thing you don't, and i agree that most of the people don't know the capabilities of the databases but your comment implied that it's a bad idea in general and i can't agree with that.
The places where you would use SQL would be for reading data and some of them (views/queries) might get big, a bit complex but i doubt the equivalent code in any other language doing the same thing would be any simpler/easier to understand. I would bet the view code would be an order of magnitude shorter than the expression of the same problem in any other language, also you can use stored procedures (in any supported language) for reading.
For writing ... you don't have to use Pl/pgSql ... use your beloved Python/Perl/JavaScript :) the only difference the code is running in your database.