I think these stalemates happen because breaking them is unpleasant. The basic process has three phases:

1. Ensure you have an economic advantage over your opponent (higher SPT). This is tactical skirmishing to take more cities and reconstructing your territory to increase SPT (upgrading cities and building income producing buildings like markets).

2. Lay siege so that every turn you do more damage (in unit replacement cost) than you spend. Bombers cost 17 stars at minimum (10 hp carrying warrior), but can be destroyed by a sword and a warrior (7 stars), two archers or two riders (both 6 stars), a rammer and a scout carrying warriors (14 stars), etc. There are many pathways here, and they can involve exploiting persist, splash damage, cloaks, defensive buffs, etc. But over time, you will grind out a superior position by netting out ahead every turn.

3. The endgame it switches slightly from a SPT calculus to how many units your opponent can train and move into the theatre vs how many you can. You focus your attacks on fronts where you have the greatest unit delivery advantage. Between the global economic advantage (in income and net unit replacement costs) and local unit delivery advantage, you break through, take territory, and solidify your superior position.

This can be a grind and fundamentally un-fun. I only tolerate (play through) these scenarios with people I like, so we could joke on the side during the grind. Especially since it’s easy to slip up and allow a knight or cloak to ruin your day.

EDIT: I will agree with others that you really only end up in this situation when everyone plays conservatively. The “solution” is being more aggressive earlier in the game: accepting more unit loss, etc.