realistically, do psychiatrists do this?
Yes
Some couples therapies books were written by psychiatrists, but one should only do it if they know what they're doing. I'd estimate the majority of programs don't teach couples/marriage therapy. If so, a psychiatrist from such a program shouldn't pretend to have expertise in it. Some programs do teach couples therapy, and some psychiatrists learn it on their own by reading textbooks on it, attending CMEs, getting training after residency, what have you.
Just because we're doctors we don't know everything.
The doc in this clip was trying to treat stuttering based on a Greek myth where one used marbles to treat it.
Just one doc out of a large group of docs thinking because he has an MD he knows everything.
Some docs have entertained a narcissistic belief that because they have an MD, they can do anything. If you don't have expertise in something you don't. I'm a psychiatrist. I still wouldn't trust myself to do an ECT (though I do plan to get more training in this area and expect to be able to do so), child psychiatry, or a whole range of things.
If you want to do couples therapy and your program doesn't teach it, attend CEUs or CME programs where you can get the expertise.