I think you hit the nail on the head when you ask how often do physicians "prescribe" this. You can't "prescribe" behavioral activation or change with much success. That's not how behavioral change really works. It makes sense to work with therapists who are going to make exercise a part of the "homework" between sessions and who have the expertise to use motivational enhancement techniques and problem solving. It also makes sense to reinforce this in your visit and use some brief motivational techniques time permitting, but typically you have too many other things to do in a session with someone who is acutely depressed to focus on it for long.
Physicians harping about behavior changes like exercise, losing weight, and quitting smoking is only helpful a tiny percentage of the time. The rest, it's probably harmful, as it likely just increases resistance if not approached in certain ways. So if you're not going to do it "right," (i.e., MI based techniques), you shouldn't do it at all.
My very prescriptive and ineffective primary care physician (whom I otherwise really like) harped on me a bit. Honestly, I did not go to a pcp about 12 years because I knew I was overweight and because I knew that most physicians, frankly, are high-and-mighty *******s about their patients who are overweight. She did give me info about a clinical trial about some computer based interventions for weight loss, and I thought it sounded like fun. However, I was assigned to the placebo arm (this must have been the worst blinded trial ever), and the PI on the study, who lead the orientation session, was one of the most obnoxious, annoying people I ever met. I lost about 30 pounds during the study because, honestly, I had fantasies that if I lost a lot of weight, I could screw up the results, make their intervention look worse, and maybe she wouldn't get her next grant funded. So, besides motivational interviewing, being really vindictive helps too.
I had a very good full semester graduate level motivational interviewing course taught by someone who wrote several of the chapters in the Miller and Rollnick book during a masters degree during medical school. When I returned, we had a standardized patient examination about weight loss. During the session, I used lots of MI techniques, and received really high marks from the SP on feeling motivated to go lose weight. But I failed the exercise. I failed the exercise because what they wanted us to do was go through a lot of information, not elicit much feedback, beat them down the throat, and make sure to thoroughly cover a few medications for weight loss that were frankly no better than placebo on a good day (and even spending most of the time on MI, I still covered 80% of their crap). I tried to explain to them why their approach was flat out bad, but the rheumatologist running the program (who was a hell of a lot fatter than me, by the way--a bunch of fat people discussing weight loss is always a nice SNL skit waiting to happen), looked at me like I was speaking jibberish. I did the exercise again, did what I thought was near malpractice, and passed with flying colors.
So your question is a good one, but "do you do it" is much less important than "how you do it." Maybe 15-20% of the population hears what a doctor says about behavior change and thinks, "hey, I should go do that." The rest of the 80% say, "I know that, *******. If it was so easy, I would already be doing it. You didn't help me at all. You really just pissed me off and make me want to go sit on the couch/smoke another cigarette/eat more doritos."
To be consistent with OPD (who is addiction trained and clearly skilled at motivational interviewing,) offering behavioral interventions on the "menu of options" of things folks can do to feel better is perfectly fine. Giving some feedback as to why you think these things is a good idea is good. But the way that most physicians do these things, by shoving them down people's throats, is bad.