I know of at least one TOC where the Ops Director had driving turns to maintain his competence.
It all depends on each company. I'm fairly sure that FGW had driver managers actually working turns as drivers quite often for a while.
ScotRail its a no-no, the DTMs have driving competency, Ops Standards nearly all have driving competency, and there are possibly others in the management structure who have kept their driver competency, but they can't drive without a driver present. Oddly though, this doesn't apply to Guards Managers (CTMs), who can (and do) work trains as a guard during Conductor shortages.
The thing at ScotRail is also that DTMs absolutely do not want to be driving trains either - most of them are DTMs because they had enough of driving or the shifts, and although the salary is slightly more than a driver, in real terms they get paid no more (probably slightly less) than a driver does. They work 5 days a week where a driver works 4, and they don't get overtime at all, just time in lieu. Oh, and they have an on call requirement too...so you can imagine, there's no incentive for them to want to be doing shifts as a driver. Not at ScotRail anyway.
Likewise at the 2 TOCS I’ve worked at, DM’s regularly relieve drivers on their way to/from work or just randomly in order to keep their competencies up
They do this at ScotRail too (well, prior to COVID). The difference here, I'm guessing, is that if you're a driver manager and you jump into a cab and tell the driver you're taking their train off them, you'll expect them to stay in the cab with you whilst you drive. Its been said before, but I think they have to do 6hrs a month and I doubt they ever go over that. Allegedly they cover every route in those six hours, but they never know routes as thoroughly as drivers do. They're quite interesting to watch actually, everything is much more deliberate and focussed, like they're very conscious of the fact they're being watched and that they don't drive very often.