The movie wasn't meant to be realistic, i have no qualms about the movie itself.
Extracted from Wikipedia
Much has been said about various 'tactical errors' made by both the German and American forces in the film's climactic battle. Steven Spielberg responded, saying that in many scenes he opted to replace sound military tactics and strict historical accuracy for dramatic effect.
source: Sunshine, Linda (1998-07-24). Saving Private Ryan, The Men, The Mission, The Movie : A Steven Spielberg Movie. Newmarket Press. ISBN 155704371X.
It was people who keep taking references from this movie as "something realistic/cool/tactical" to add in the game. Which is pretty disturbing, as i regard it how much Hollywood has destroyed people's mind about WW2 action.
BTW, let's get back to the topic.
On the balancing issue: you complained about ppl on panzers capping flags by camping then whoring all around with his/her uber mechanical device. I guess that what makes a tank... a tank. I was never too afraid of tanks back in vanilla or any other games than in FH. In addition, i was never too afraid of AT soldiers as a tank driver in any other games than in FH. A correctly placed shot could finish my tank quickly. I think it is well balanced.
IMO, tank is very expensive vehicle, it is valued quite highly on the battlefield. So its depiction in-game should live up to its real world counterparts... a fearsome fighting machine. Moreover, back in the days of FH1, we live up to what is known as grenade spamming (stand near ammo box and start tossing grenades in endless succession). Thus in FH2, many kits don't carry grenades and some have very limited amount of grenades (compared to vanilla and many other games). This doesn't mean to make the hand grenades so special. I think, the availability of riflenades to every rifleman (except for Italian) itself is a bit beefing infantries up.
Now, present your argument about why AT kits like Bazooka/PIAT/PzSchrek/PzFaust itself isn't enough. But i guess, in the later stage of the North African theater, where we still have the obsolete AT rifles to fight up-armored Panzers makes the AT kits kinda useless though. I can agree with your suggestion in this part only.