Its something you are going to have to get used to with the new clans system. Each clan has multiple family members who can all lead a party when one of their members loses their parties, for each faction your going to have about 27 parties you have to actively fight and ~20 reinforcements that can start new parties when an active party goes down (and thats before each factions ~20 kids at the start of the game grow up, plus any newborns throughout the playthrough). Just have an understanding that the average army has maybe 5-10 parties in it, so you have to defeat 3-6 armies to get through the active parties, meanwhile reinforcements will start new parties when their family members get defeated and will take troops from their garrisons and start recruiting new troops often on their way to their next battle or army formation. So really your going to have to defeat 5-10+ armies to even start making a dent into their garrisons plus whatever they can recruit from villages. Bannerlord is slog of constant battles and a single large fight will make little difference.
If you actually pay attention to the story the empire hires other factions to help with their battles, like how they hired the aserai and vlandia to help against the battanians and sturgia. The aserai got slaughtered and the Vlandias decided not to help once they saw the battle start to go south. But the empire has always outsourced its fighters, so not sure what your point is there. Regardless of lore they are going to do their best to maintain their party levels whereever they are located, so if they are traveling through batannia to fight vlandia they are going to pick up some batannian troops.
