My thoughts exactly. I don't do a ton of DB programming, but I've only ever written one thing in a non-agnostic way. We got a requirement that users wanted to copy an entire "project" which was the top level of a hierarchy. I wrote an Oracle routine to do the deep copy. I did it because I imagined what the PL/SQL would look like (clean) vs. what the Java code would look like (considering Hello World in Java is ugly, you can see where I'm going ;-)
Mine too! Having logic embedded into SQL functions seems to be an anti-pattern to me (it's harder to maintain and harder to do release management). While it's great that Postgres can do this (btw, I love Postgres), I suspect there aren't many people will use this feature in production environment.
I used to think this, but have relaxed that view over time.
For constraints, validity checking, things like adding/updating timestamps, and other things that are about data integrity, about the only time I don't do that in the DB is when outside information is involved such that it can't be. Otherwise, to the extent possible, I want the datastore to only accept valid data. This goes to the notion that fixing code is easier than fixing data, so the store can not only defend itself, but also help catch bugs.
There are also times when dealing with huge amounts of data that doing whatever you're doing in an SP is the only way to get decent performance. Dragging enormous tables over the network to process is sometimes really wasteful. If you're tuning indexes and whatnot against that model, you're already changing the DB, and doing so at a level that is implicit rather than explicit, and in ways that can change out from under you (if the statistics change).