I am a print finisher in the UK and yes we still do a lot of business cards for people. More often than not these days though it tends to be more high end finishes things like foiling, duplex or triplexing with different coloured stocks, round corners etc.

Ten years ago and back we did a lot more high quantity shitty cards but I also worked in a more generic print place then so they may still get pumped through bigger places.

I’m actually foiling some business cards right now xD