It'd definitely help, but then you're creating a almost wholly doctrinal tech tier.
The main problem is the heavies do everything right now. They've got the anti-tank firepower of a tank destroyer, the anti-infantry firepower of a late-game anti-infantry vehicle, and a ton of health and armour on top of that. All for the cost of two medium tanks.
They're simply just more cost effective than their price in other T4 vehicles.
Personally, I think the solution is to put that proposed sidetech cost on the heavy itself. It'd have the same effect on the first heavy, and serve as a penalty for losing them.
It's also much more straightforward to implement.
Don't forget their biggest Plus :
you don't have to micro multiple units
I dunno why people forget that so often