So for Romans the bIacksmith have double the effect for infantry to compensate for this they lack Platemail Armor, supplies, gamberson. In castle age with FU infantry you get +4atk and +4/4 The equivalent of the Burmese, Malians, and double the Teutons bonus. It is worth noting that each of these civs gets these bonus for free but that is still insane. Their longswords are missing supplies and Gamberson but
they also get a buff from nearby Centurion +10% speed and 25% attack speed.
For the imperial age they get +8 atk and +4/4. For their halbs they get the equivalent of Garland wars and 1MA and they get this while actually save on Plate Mail Armor. Legionnaires are a bit of more tricky to compare their upgrade cost +50F 50G more than champion but they also skip 2HS, 15F per unit is not as big of a deal in imperial age, They get 12+8 atk and 2+4/2+4 so they are basically the Equivalent Burmese and Teuton Champions combined. you also save 675F 375G on upgrades but have to pay +15F per Legionary compared to other champion lines this *might* be balanced.
Except I’m also ignoring the Centurion bonus which increases to +15% speed and 33% attack speed with elite Centurion the equivalent of Celts with Squires and Japanese combined. They also get Comitatenses which give Centurions and Legionaries +50% faster creation and 5 charge damage, although it is an expensive tech.