I don't think the later pikemen actually physically pushed their comrades. Or at least what I've read of them doesn't suggest anything of the sort. "Push of pike" AFAIK rather refers to the two pike blocks "pushing" against each other until one broke under the pressure.

Mind you, they also found out during the Thirty Years' War that "thin" pike formations were quite the equals of "deep" ones head on. There would doubtless have been a difference had the clashes been drawn out into attrition matches, but that wasn't how infantry battles were normally resolved by that time - and when they were the attrition was supplied by massed arquebuses and regimental artillery blasting at each other at uncomfortably short ranges. As might be imagined the senior officers hated that sort of developement as much as the rank and file, as it wasted a lot of trained men for very uncertain outcome...