But he's been careful not to conscript from the big cities, for political reasons. He could raise a lot more conscripts... but there would be political consequences that he probably wouldn't like.

So there are real constraints on what Putin is able (or at least willing) to do.

Also, AIUI (and I could well be wrong), he at least says that he's not sending the conscripts to actually fight in Ukraine. Whether that's actually true... I have no data.