Czech Post has an app that does. Local price is like a $1. It works worldwide regular international price.
https://www.post.ch/en/sending-letters/sending-letters/postc...
The documentation says you must buy either 3 postcards or 10 from within the app. 3 postcards sent internationally cost 168CZK = $7.64.
3 postcards sent to the EU cost €6.34.
One example I just found. £2 to address in UK and £3 international.
A thought has crossed my mind: if these kinds of site are quite common across the world and charge lower rates for sending cards within their local country, perhaps there is an opportunity for someone to set up a central Web site that finds you a local service? Add a small percentage?