What are you calling professionals? Because early mercenary spearmen do quite well unless taken a full charge when they aren't braced or in good formation. They will still lose to most cavalry though because even if they take 1/3 losses on the charge, then in the melee they kill 1/2 the cavalry but lose another 1/3 and rout leaving cavalry having defeated a unit 3 times size with only 1/2 losses.
As for Norman cavalry or Byzantines I made an exception for those because we actually have reports and witnesses from some of the battles that talk about a relative handful of Normans defeating 10x their numbers in a charge and often it wasn't just infantry but other heavy cavalries defeated. Byzantine charge is strong but not as powerful as others but they kill huge in melee after with very few losses more than offsetting slightly weaker charge which seems about historically how it occurred at least when the Byz were able to field sufficiently trained, motivated, and equipped heavy cavalry which much past 1100 they were never able to do historically and instead relied on mercenaries.
Due to the game mechanics whether the infantry rout or are killed in the charge has little difference except to the amount of losses the cavalry takes. Right now if an infantry unit takes a charge and fights alone vs most heavy cavalry they will lose and barely hurt to 1/2 hurt the attacking cavalry. If they get some help from another infantry unit though the attacking cavalry can often be driven off with 3/4 losses and neither infantry routed.
Newest RC which PB will release when he has time reduces charge of early cavalry. I agree with you that a good cavalry charge basically evaporating 90% of an infantry unit in 1 second of charge contact is bs. However- even if reduce it so full charge only kills 30% on contact the cavalry still probably going to rout the infantry if the infantry doesn't get help. Just with a few more losses to the cavalry. So what I am saying is yes some things are a bit unbalanced but making them better balanced doesn't mean tactics can or should be ignored.
Numbers alone don't make much difference. Since I've read lately alot of posts on TWC talking about rioters I'll use that as an example- there are often only 1 riot police per 10 in the crowd yet the riot police almost always succeed in dispersing the crowd. Yes equipment makes a difference but the biggest difference is in training and leadership. So having a group of knights riding warhorses trained since childhood to fight making a bunch of men who only started training to fight as adults(assuming professionals here) that don't have equal equipment, training, or leadership is not so amazing. I think the motivation of both groups would be equally strong but infantry need to cooperate to survive and thus discipline and leadership need to be actually stronger than an equivalent cavalry unit which once the charge is completed don't have the same loss of initiative breaking formation to ride down individual or small groups of infantry which stopped acting as a cohesive unit.