This is a fantastic conversation, and I have to admit that I've been thinking about this topic myself. However, I realize that I've actually been playing games battleboard style before it was incorporated into the rules. When you're playing an encounter where you're just moving across town to meet someone for a job offer, or when you're in a tavern chillin', moving your group and PEFs on a map seems to be the wrong tool for the wrong job. A lot of my games, in fact, have been just me sitting at a table, dumping a bunch of d6 in two -- or sometimes more -- colors, and playing an encounter using the dice as figures (turning the numbers up to indicate Rep and weapon target rating). The dice don't move; they are positioned against who they're attacking when battles break out. Often, I don't even crack open a rulebook; I'll just wing it based on what I recall from the various tables.
But there are times where setting up a map, whether using grids on a spreadsheet or drawing them on a wet-erase battle mat or sheet of paper, enhances the action and the narrative. This is especially the case where you're raiding an enemy base, facing a final boss, or foraging for supplies in ATZ. The activation system where it's frequently possible for each side to miss turns due to rolling their die higher than their rep amps the tension. There is nothing like trying to flee a firefight where your activation rolls pin you into place for a turn (or several), watching helplessly as zombies amble towards you, or escorting a prisoner in Six Gun Sound while a pair of outlaws sit perched on a far hill and don't move. What happened on that last example? I imagined them arguing with each other over the best course of action to take.
I also like the ATZ use of activation for triggering random events. In one scenario I introduced to my nephews, we each selected a random event for me to list on a table. The scenario was to travel to a restaurant to eat dinner. My older nephew suggested "poop in your pants" to add on the list, and I gladly did so. When we arrived at the parking lot and got out, a PEF resolved into gangers attacking us. A random event triggered, and the poop event was rolled. I randomly determined which one of us pooped, and it was the nephew who suggested it. It was hilarious, and I determined it would give us a negative modifier on getting a table once we got inside. We never did because we got wiped out, but that's another story.
But the non-tabletop way of playing allows things like Larger Than Life scenarios to flow from one part of the quest to the next more smoothly. Playing the action in the theater of the mind can fill in a lot of the blanks, and I'll often use more challenge tests and other non-PEF related activities than I would in a tabletop setting where I have a focused objective in front of me on the table to achieve.
Another area I have mixed feelings about is phasing out the testing for successes (roll Rep number of dice +/- modifiers, with 1/2/3 being successes) in favor of rolling 2d6 (with modifiers for both number of dice and Rep) and comparing to see which side has passed more dice. I think successes works really well for opposed challenge rolls, especially for Talk the Talk. But making the switch in melee combat has resulting in battles feeling pretty much the same, so the switch didn't feel so bad in this case.
What's really exciting about the new releases, however, is that we're now getting battle boards and counters in these rules, and the newer rulesets are including both generic encounters followed by a generous set of prewritten encounters that are a lot of fun to play. If you're already familiar with the way the mechanics work, you can quickly review the rules and start playing very quickly. In fact, I've often procrastinated in the past with playing table top style, where these latest rules have resulted in me dumping out my dice and diving in.
In the end, it's all about having a nice tool chest of options. Hopefully, all options will be made available for players to use what works best for them.