It wouldn't. Monchug is one of the younger rulers. By time he dies, the Khuzait parties and armies aren't actually any faster than other factions, because they have so many non-Khuzaits troops and parties. Instead, grind everyone else because they have more troops, more influence to continuously generate new armies, more parties, more settlements, etc.
Like, it isn't unusual to see Khuzait faction armies being like 2.1 move speed in 1110 because the army has like 2,700 dudes in it. It still works though, because it can siege or raid wherever without anyone interfering.
It is not just about the army speed itself. It's also about the individual party speeds when they gather the army. I watched many times Khuzait armies moving to attack position with few parties in and the 70-80% of the remaining parties joined them very close to final destination. There were also cases when non army parties with high speed joined the battle just because they were near and could make it due to their high party speed. Lets say the 70% of core Khuzait army is average speed. It's enough if few parties with 150 - 250 (usually 3-4 parties in total of 500-800) are moving above the average speed and they can support the core army anytime when it's outnumbered.
Regarding dominant faction power... I intentionally tested this when I helped Vlandia faction to reach 25k vs Khuzait 16k power. Vlandia had more fiefs, more clans, enough time to train higher level troops in peacetime. Yet still when I gave free run to Vlandia vs Khuzaits, Khuzaits were able to gather always bigger armies later in the war and eventually increased their power above Vlandia to 20k vs 14k. I intentionally watched the battles and the army gathering to understand how is this possible (joined even Khuzaits by cheat console to observe when the army is created and how the parties move). Their armies are basically always gathered with higher numbers as the opponents army and I am convinced it's because of their speed. I can be wrong but that is my perception.