Actually, I think you are right, and this is probably what it is. He did gut a lot of those agencies and send them to the front fairly early on - there were police officers, firefighters, national guard units, etc. that were a part of what would probably be some kind of surge, and they were complaining about it. I recall the OSINT people pinpointing the actual units (like a highway enforcement unit, etc.) and talking about how crazy it was that these people were in Ukraine (I don't think they were necessarily front-line fighters). We were seeing patches, etc. It has to have been a year or two ago though, because this year, it seems that all we see are just large numbers of soldiers that are ill-equipped and worn down.
When Prigozhin made his little move on Moscow, there weren't a lot of national guard units available to block him, because they had been gutted, which is why we saw your typical city cops digging holes and positioning machine guns.
If you are in the reserves and they call you up for one of these units, you would definitely take that versus going to Ukraine, and Putin needs them because:
They probably didn't need a lot of those jobs at home prior to this year (don't need as much law enforcement if you send criminals to the front) and the "national guard" units are about protecting the government and infrastructure, not protecting Russia the nation, and so they didn't need to backfill them. Things are now reaching a critical mass where the Ukrainians are probably close to the kinds of strikes that can leave parts of the country without power and fuel for longer periods of time - Russia only has so many replacement parts for those refineries and power plants and can only patch together so many systems.
And if air defenses continue to be worn down as Ukrainian production ramps up, they are going to need dudes in pickups with machine guns.