My reasons for not using time limits are:

I don't use time limits as I like to play the battle out to the end.

In the field as I use mostly all cavalry armies, one good spot can quickly be substituted with another. Also playing defensive with an all cav army is not the same as playing defensive with a balanced or mostly infantry army. You move anyway, and almost never stop, except to shoot, then you move again. Usually you don't hold a single position but many and force the enemy to react. Sometimes you do get nice cliffs, so you go up there shoot as much as you can and then move. Point is you're not stationary long.

I also feel that I can win otherwise unwinnable battles with the time limit. I can just run around the map as defender until the time runs out. Though I actually don't do that, but I feel tempted to .. lol.

I rarely let an enemy siege a city, I always catch the enemy army outside and cut it downm before it gets to it's target.

If, on rare, occasion, an enemy sieges a city it's usually met by a relieving army from outside the city. If, on even rarer occasion, an enemy assualts the city, I have'nt seen the AI loop bug, or just standing there, I usually end up attacking anyway.

Lastly I like to take my time and I don't want to be looking at the time.

For me the time limit is a negative. I don't like it, never use it.