You know that is the text book definition of a straw man argument yes? I said I don't think it should be able to push, you can remove it's ability to push with how further nerfing it's health and durability!
You are being pretty dense no offence. Here is the deal, People are not upset about tank or light vehicles they cost something and generally put themselves more at risk. the hq trucks pushing are dumb because there are no staring fuasts to get rid of it on the allies side. It is also a free immediate map redesign tool that can get rid of cover you don't want. The most frustrating thing is how this truck can push however. Like you said earlier, Pushing disrupts the infantry making them do less dps. Truck push moving rifles or conscipts allow volks to win in a 1v1 situation which is completely unfair.
The next big reason is why the hell does OKW need a truck to spawn at the beginning? It should spawn when you have the fuel to upgrade it, there is literally no point in having it on the field before that other than to irritate players with truck crush.
I understand you don't like the idea of crush in general which I understand. However, your solution of getting rid of crush would amplify the blob problem immensely. Tanks can currently stop shrecks from wiping all tanks by moving them around, so for gameplay purposes its needed. Panzershreck blobs and zook blobs would be unstoppable by tanks period without crush. Just imagine two volk squads trying to kill a T34. Your expensive tech tank can fight against this now due to crush, however it would not without it (You'd never kill both squads in time to stop the volks from killing the tank).
So while tank crush can be silly, for gameplay it is currently fine with the exception being the free immediately spawning truck with plenty of health to win early game engagements.
Just like the OKW base flack emplacements, there is literally no reason to support hq truck pushing.