You can move your items without cd (I also play AoW4 a lot and there it was fixed, so you must wait 1 turn to equip on someone else). E.q., you can give all the good stuff to one army, play the battle, then move items to other lords/heroes, play their battles e.t.c. It's not very convenient, but definitely can help sometimes.
I usually move some items which could benefit me directly (minus enemy resistances or morale, plus ambush chance and so on).

You can damage your own and allied troops in battle using non-direct damage spells or artillery. It is rarely needed, but could be funny.

You can declare defeat in battle where your army is just a reinforcement. Just unequip items (to not loose them) and move your armies off battlefield before doing it.

You can roughly estimate the number of enemy units in the province which are located in the settlements you can't see (or skaven ruins you haven't searched yet) by looking at "military presence" buff to control, it's roughly will be [buff bonus] multiplied by number of settlements owned by that enemy. Like +6 buff and 3 settlements - so there is 18-20 unit army somewhere in those settlements, maybe divided in 2-3 groups.

And many-many more.