It is also true that this unit is one of the strongest general units early game (if not THE strongest) and very hard to die. It is the way you use it. The AI has the tendency to always focus your general when is exposed. So if you choose to put him in the front line and have him charge heroically or being charged by a zerg of enemies then yes possibilities are the unit will get swarmed and finally the general himself will fall. Because losing your general has a dramatic effect on morale most players choose to use this unit carefully. That doesn't mean he won't fight at all but
ideally he will fight when and where he can turn the tide of a battle in balance.
Bonus video of
a custom battle between a unit of Hippeis versus 2 units of Custodes Praetorii (maybe the strongest Roman infantry general?).
What you write about cavalry is what happens often but not always. General cavalry units (and shock cavalry in general) get very good scores against medium infantry, or most "non spear infantry" because of their charge bonus - even charging head to head. Give it a try some time.