Personally I'm a big fan of the morale/Flag system in Skirmish and its a bit sad that capturing or defending Flags are not included in the score system. So it's not worth for the most people to capture any flags, only charging into the enemy without any braincells just for the score. This would also support infantry players for better scores because these are normally defending flags.
The apex legend score system is good but should be not giving you high rewards, only a small addition. The reason for that is your only objection is to make killls/assist in Apex, in Bannerlord it isn't. With different classes ( some have a much higher dmg output that others) this would end In massive spam of these strong classes. Without class limits this will not end well.
Oh and MMR decay should be a thing too so people cannot sit on their high rank after calibration and then stop playing and staying on top.At the moment Players who are doing this are playing with alt accounts so they can play without loosing their precious rank.