Rome did not just use Heavy infantry, they used cavalry who was as good as their opponents as well as skirmishers and light infantry. Roman army was not monotone Heavy infantry army but more diverse with different specialist units.
All right, we need to take a step back here:
No one argued that, but as pointed out: the proper "roman" cavalry wasn't that good, not bad, but nothing special either - so they used axuillaries or allied forces for that. And yes, like all other nations they used spear-throwers/archers/skirmishers/scouts. But they were never the backbone of the roman force. The backbone was always the (heavy) infantry.
The roman cavalry forces were soundly beaten in every single clash against Hannibal, with the exception of Zama, where they had managed to sway the numidian allies of Carthage
B) the romans still managed to take over most of the known world. How?
It was not because their generals were better, they werent.
It's because they adapted to, or appropriated, everything that was better than their style of doing things. When they realised hoplite formations weren't as effective against their enemies, they adapted their fighting style. When they realised that style weren't as effective against Phalanx's, they adapted once more. When they got soundly beaten by Hannibal, they once more adjusted their formations. When they met better equipment, they took on that too. And it goes on and on.
How would you model this? It can not be made on an army to army basis, as this was something that happened across all of them. The average Roman (heavy infantry) soldier wasn't a god, but their equipment was usually of high quality, and their training and tactics were usually a lot more flexible and generally more battle tested than their opponents.
This did not make them invincible however, as has been pointed out, but generally when they were defeated, it was due to their system of generalship being a bit of a gamble, meeting something new (elephants, phalanxes, Hannibal, Cimbris/teutons etc.), or just mere chance.
Whether you want it or not, the backbone of the roman army was their heavy infantry, and it was some of the best in the ancient mediterranean. How to best represent this?: bonuses to their heavy infantry.
Besides, as pointed out by
@Voigt - it's in the latin group
I seriously don't get the point of this being brought up for discussion? Military traditions need to give bonuses in some way or the other, and heavy infantry bonuses for the roman/latin armies is the most logical way to go..