Yeah! That sounds like the title of someone's thesis or something, but this post won't be as dry as the title suggests...
As stated in the title, I've been running combat without a battlemat in my Wilderlands campaign. I chose to do this for multiple reasons, the least of which being that it eases play for me. Without the map present, I'm able to make quick judgment calls on flanking, difficult terrain, distances, etc..
This makes combat quite a bit faster than it normally would be, since nobody really has to count squares, move their mini, recount for distance to get modifiers to range, and so forth. Any questions can be asked on the fly, and everyone at the table is intelligent enough to make adjustments and ask for more detail, if needed. There is also the fact that I don't have to draw a map, which I think is one of the biggest problems that miniature/tactical combat has when it comes to time.
In our experience so far, there have been only minor hiccups as the players (who are used to battlemats) adjust to having to imagine their combat areas and remember conditions of the field, and not have a quick reference to look at. It's running fairly smoothly and we're able to fit more into our game sessions because of it.
In any case where I can make simplifications, I certainly try, and I've taken to heart the mantra of "Say Yes or roll the dice," that has been prevalent in what used to be the OSR.
Do I think that Pathfinder, as a whole, is a simpler system-fix than 3.5 was to 3rd? No, but there is quite a bit of streamlining that I can work with to make the actual mechanical elements of gameplay cause as little friction to the flow of the game as possible.
I, admittedly, don't have anything solid to add to that, because right now, I'm learning, too. I'm considering the changes Paizo has made, taking in all the fascinating rules that are out there in the blogosphere, talking with anyone I can about my game, and even looking at non-Pathfinder/3.x games and systems to see what I can use to make my game easier.
Don't get me wrong, I don't want a simpler rules system. If I wanted something simpler, I think I'd be running Labyrinth Lord or Moldvay Basic (since it's what I own...I'm told Mentzer's edit is better, but *shrugs*.) It's nothing like that. I love 3.x, and what Pathfinder has done with it. I like the complexity of rules that it offers, and the customization I can achieve with it. Nobody can convince me of system dominance at this point.
No, what I want is to perhaps tweak what rules I do use to create just a little more transparency. More on this to come, but I have some prep to do right now, as tonight I run my Wilderlands!