The mount was not as heavily armored, however, as modern armor vehicles are, and extremely vulnerable to pikemen (as many other commenters here have brought up: the landsknechts).

Back to the analogy, a peasant (in the modern sense) is unlikely going to be as able to obtain an anti-tank or armor piercing rounds as easily as a peasant (medieval sense) could pick up a pike.

You need a disciplined pike wall that is so cohesive that it does not break! You dont get magical superpowers by just picking up a pike (like you wont become a good programmer by acquiring Borland Turbo C++). You need to train with your comrades.

A modern civilian doesn’t need to penetrate a tank, just get it stuck and light it on fire.

The same applied to an armoured knight, but it's hard to trap a mounted warrior when you're on foot, just as it would be hard to get a tank stuck unless you know what you're doing.

I'm certain that more than one knight died locked inside a burning barn back in the days.