Originally, I was just going to edit the last post but I went off-topic from that post.
The number one problem with moving units on the map is GM management. Needless to say, most IOTs don't need armies moving on the map to be effective. RIOT, IOTVI, Iron and Blood, Tropico, and many other IOTs didn't require units to be placed physically on the map and those got along just fine. There are a few problems with pooling armies.
1.) Ultimate Defense. I'm going to use Khitan from RIOT as an example. Needless to say, there was no realistic weakspot anywhere in Khitan's Armed Forces because they had so many of them. These army units can defend any place and the only two realistic ways to beat Khitan in this case would be either a dozen coordinated strikes everywhere to divide their forces or nuclear war. The problem with this line of thinking is that there is no reason why attacking Khitan China should be just as difficult as attacking Khitan Israel. After all, Khitan sent hundreds of it's armies into the Middle East but now these troops are able to defend in China at whim?
2.) Less Strategy Involved. Let's take Khitan as an example again. Say that they had 300 armies and I attack them along three territories that my country borders with a 100 armies each. Now, let's say I'm using the middle army to blitz. Besides the ungodly number of dice rolls (which are less of a problem), there's less meaning in "breakthroughs". Say that the 100 v. 100 battles were to the death and there's a blitz. What happens is that the middle army can simply charge through and probably get a lot of territory for free since, for some reason, armies don't pull back. However, say that units do pull back, then is it really a breakthrough? I figure the GM could add and explain the mechanics behind all of this (including the inevitable math) or simply make units something to be placed on the map.
Yes, blitz could have a limit on them but it shouldn't take several years to charge through a territory after you broke through front lines? I suppose if you take supply lines into account but again, armies on the map are still better for that.
3.) No Grand Strategy. IOTs where buildings are placed in territories go nearly hand-in-hand with IOTs where units are placed on the map. Especially if said buildings are just forts and fortifications. When armies are pooled on a map with a large number of provinces, fortifications mean nothing. What's the point of building the Maginot Line can shift his entire ARMY to going through Belgium one turn and then go on the defense and hold at the border, despite having shift his entire army into Belgium last turn? It's one thing to use your armies to assist an ally in a war. It's another thing when your armies will still be over there the next turn. Another thing further if you have to get your forces there in force in the first place.
Units/Defenses on the map+Zone of Control is great for Grand Strategy on a large province count map like the RIOT map. ZoC isn't require on smaller maps like Iron and Blood and Cold War.
What does pooled armies have going for it.
1 (and only).) Simplicity