I think this is a bit of an old wives tale, possibly origination from "olden days" when maybe it was a problem.
Quote from the Telephonics RDR1600 Pilot Handbook;
The design of the system is such that full operation is possible
approximately two minutes after turn-on. Therefore, the pilot may
choose to leave the function switch in OFF, rather than STBY, if no
significant weather is in the immediate area of the aircraft. The life
of the magnetron transmitting tube will be extended by leaving the
system “OFF” when possible. This, in turn, will reduce the cost of
maintenance.
I enquired of two senior, highly experienced avionics engineers in my last company and neither of them had ever heard of radar gimbal bearings failing. They did not think the radar would be damaged by switching it off.
In my case, the subject came up because we had a couple of aircraft which suffered from r/t interference from the radar on a particular VHF frequency and the short term cure was to switch the radar off.