I like the attrition idea...
...
if there is a possibiity to counter the attrition. By a very basic supply-system, for example.
Of course you have full supply when inside your own cultural borders.
Then, there could be a new supply-unit with a supply-range of, say, 3 tiles. All units in this range don't suffer attrition; leaving it, they do.
This could be be expanded, too: Limited (50% of normal) regeneration when outside any supply-range might be possible and - when using the "healing-promotion", a loss of the turn instead of the usual "instant-heal".
PS: I'd say always note the gameplay benefit a new system should achieve
That's better than just "realism".
I aggree 100%! Therefore:
In my imagination, a system like this would force the attacker to plan ahead his invasion and protect his supply units carefully.
The defender, in contrast, would want to take out the supply units to weaken the attacker and slow down his advance.
I think, this could be challenging and quite fun!
At equal forces and without surprise attacks, attackers are still disavantadged...
And this is, how it should be! After all, the defender fights in well known terrain and with short supply lines. When besieging a fortified city/casle, a 3:1 supremacy was needed, as I did read somewhere (IIRC).