1) Cataphracts were not "knights before the invention of stirrup", they were infantrymen with spears who were uppity enough to get on horses. Seriously, their main tactic was to hold their spear in both hands and poke their enemy while
slowly riding towards the enemy. This is, like, complete garbage. Medieval knights were actually game-changing, with their ability to crush infinite amounts of infantry by charging, cataphracts were just losers invented by people who didn't know jack about proper cavalry.
Also lol on "skirmishers busting people up from the distance". Even thought why skirmisher weapons, like javelins, went out of style with the advent of Medieval Europe? Because they're garbage. Literally useless garbage against knight cavalry.
2) Roman artillery was, comparatively speaking, shit. No seriously, it was. Even thought why people unlearned how to make all these fancy ballistae and catapults? Because they were actually useless in medieval siege warfare. I can't believe you think that these dank little machinas:
are better than these MASSIVE TECHNOLOGICAL CONSTRUCTS:
against typical Medieval European fortifications.
Like, there's a fucking reason why Constantinople was mugged by Medieval Europeans, and not in reverse. Actually, there are multiple reasons here, but one of them was definitely the fact that Romans were shit at contemporary siege tactics and so were unable to even take over a single Medieval Europe castle.
As for "better doctrine for using siege weapons", proper Medieval European cavalry make Roman field siege engines a prey to be slaughtered, and proper Medieval European archers/crossbowmen are literally better at the job of fire support that them. For one, they could actually do significant damage to knights in certain circumstances.
And for "flamethrowers", Medieval Europeans had fucking several stories high walls for a reason, you ain't doing jack to these with your puny flames.