ORIGINAL: king171717
What do you put in your panzer corps for support?
As Xhoel explained, if you keep your corp HQ to support level 0 and all their higher HQ's are unlocked, SU's will go back to one level higher (Army HQ) before the next supply phase. This way, corps HQ always remain light, and that is true for panzer and also infantry corps. So you can put whatever SU you want in corps and this automatic movement doesn't cost any Admin points. If HQ's are locked, then it's another story, the SU's won't go back to higher HQ's and then yes, it will have adverse effects on supply of the corps HQ hosting them, panzer corps paying the worst cost, both in AP's and trucks because every SU becomes motorized in a panzer corp.
Whatever the power of the attacking units, the effects of SU's are always a welcomed addition in an attack. By example, artillery creates disruption BEFORE the attack, and disrupted elements are left behind in retreats and routs, so there are more casualties and/or prisonners. Also artillery preparations can bring down forts level before the attack and so on.
You can find more info on this in section 7.7.3 of the updated Manual v 2.5.5