PL/pgSQL function plans are cached. Functions written in other languages may not be, I don't know, but in my experience PL/pgSQL is the most widely used.
Read your link. They can be cached. You have no way to ensure that they are. And you have no way to have the planning done up front at all, you have to wait until the function is run, and even then every code path in the function has to be exercised to get it planned. And then half the time it doesn't think it should bother to cache the plan anyways. And it is per-session, not shared. So every single connection has to start over with an empty cache every time, and there's tons of duplicate plans in the cache wasting space. Not cool, and by far the biggest thing keeping a ton of "enterprise" customers on SQL server and oracle.
You have some valid criticisms of the implementation, though pgsql-hackers has their reasons (http://www.postgresql.org/message-id/CAHyXU0ybwZZUbuQQVFQMK3...) for the way things are. Regardless, my point is that the situation is not so bad as "Every time that function is executed, it is re-parsed and re-planned."
Of course it has: http://www.postgresql.org/docs/9.3/static/sql-createfunction...
And you can choose between 4 languages: http://www.postgresql.org/docs/9.3/interactive/xplang.html