Because with faster manpower recovery the combat system would just turn into EUIII, and the same problems of armies often having no hope of escape from an approaching enemy would remain. As Muscowy I had a 5k stack on the border of Lithuania, and a Lithuanian 23k stack was approaching. As I could not reach any other province before the Lithuanians arrived, I had no choice but to delete my army in order to avoid warscore losses. This makes no sense. Why, realistically, could my troops not evade them either by sneaking out of the province or entering a walled city? Same problem occured with an enemy army retreating from me in the direction of Moscow. I had a 1k artillery regiment there that had been just built. It also had no way to evade or escape, so it was instantly destroyed.
Essentially, the problem is fortresses and armies are entirely separate entities in EUIV, and Paradox does not represent the symbiotic relationship between the two. That's what should be changed.
Jomini is exactly right to say that the problem is that warscore from battles are too low and that the AI is too slow to make peace. I was going to make that point earlier but I figured my initial post was far too long to begin with. The problem is balancing it so that the higher warscore from battles doesn't encourage the chasing of enemy armies deep into their territory in order to repeatedly defeat them. Hence the need for many of the protective measured mentioned in my initial post.
The best system would be one in which an attacking country has to go to great lengths to take the province(s) they're fighting for, but that once they are taken they are likely to get them in a peace deal before very much time has passed. Wars should not often result in the complete destruction of one side's armies.
You're proposing a series of changes that make it much harder to catch defending armies and much harder to defeat them. Field battles have a large luck component, so basing too much war score on them could have bizarre consequences (an utterly defeated nation, with no surviving armies or provinces, has a large positive war score because it did well in the initial field battles). Unless there is some major compensating factor - e.g. much higher warscore from completed sieges - this will cause severe balance problems. I do like the idea that a defeated defending field army becomes sieged - presumably making direct assault very difficult, but also presumably accelerating the "starve them out" factor. This makes a lot more sense than chase-across-the-map. But I very much dislike the prospect of having to do click-and-cancel repeatedly as a large defending army repeatedly threatens to engage my sieging armies - especially if I can't catch them if they run away. That sounds like extremely fiddly game play that the AI won't be able to do nearly as well as a person would.