I'm wondering if that mobilisation isn't worse than a band-aid. I think it might actually be hurting Russia's ability to fight this war, for the reasons you state, and because it's putting more stress at all the weaknesses of the Russian military: logistics, command and control, and morale.

Those people need to be moved to the front, more food, ammo and fuel needs to be moved to the front, and Russia is already struggling with logistics. Their command and control seems to be a mess with Wagner and the militias operating independently from the Russian army, which is short on officers, and each branch blaming each other for all the failures. Adding more untrained troops is not going to improve that situation. The impact on morale is probably obvious.

Best thing to do with those conscripts would probably be to put them in trucks and let them drive more stuff to the front. Or in factories to make more stuff.

Best thing strategically for him would probably be to withdraw from all those recently "annexed" regions and bet everything on keeping Crimea. And negotiate a deal to trade all of that land for recognition of the annexation of Crimea. I think Crimea is really the best thing Putin can possibly get out of this war. And even that is hardly certain.