Well yes, that's what you'd expect. Most of the doctors I've seen at the government hospital were relatively young, no doubt seniority is a factor when applying for private hospital jobs.
I stand by my statement that any doctor can prescribe Xanax (as an example), though, and the low cost and convenience of government hospitals mean that in the worst case scenario, you've wasted 1000 baht and a couple of hours of your time.
For somebody suffering from acute anxiety, he may be more likely to go through with a cheap and straightforward course of action (government hospital) than a more expensive and complicated course of action (tens of thousands of baht, appointments with psychiatrists etc).
If he has plenty of money, absolutely an expensive private hospital would be my recommendation. I was just presenting an alternative.