The best change would be to put it in T2 REPLACING the 222.
That way the mobile defense build has another small nerf.
That's an interesting idea but I don't think it'd kill it that hard. You're only going to hit the button when you need the Puma, so you can still use the 222. If you need to replace 222s you can use 251 flamers provided you've got the munitions of them.
Yes it supplements the light vehicle play a bit too well, but I don't think that's the doctrine's fault.
The core problem is most likely the cheaper 222, making a light vehicle AI/AT army a bit too cost-effective.
It's completely the doctrine's fault. Mobile Defence was king of the Ostheer meta before SBP because of the stronger Command Tank aura.
Ostheer has relatively quick light armor that's countered hard by light tanks (AEC, Stuart, T-70). With any other doctrine overinvesting in OST T2 is risky: every light vehicle gives you an advantage but delays T3, lengthening the window where the enemy light tank rules the field.
The call-in Puma counters that light tank, allowing you to go heavy T2 without the risk other commanders bear in doing so. That Puma isn't tied to tech, allowing you to field two for the price of tech plus an enemy medium tank. Pumas can deal with their weight in everything short of a heavy tank, which is why the KV-1 of all things is SOV's shock unit against them.