Hmmmm. They have a lot of ideas there! And I have... not enough time to read them all, not tonight. I can't find the post in question, so just to talk about adding damage in the way you've described:
Pathfinder is... interesting in how the spellcasters and the martials compare. Spellcasters tend to be powerful not because they do bucketloads of damage (although they can, it tends to be one of the weaker approaches) but because they have answers, particularly at high levels, and martials don't get many answers--they just get increasingly more damage, without too much ability to affect problems that their damage can't fix. An archer, for example, can take feats that increase the damage they do--rapid shot, deadly aim, manyshot, and so on. A high-level spellcaster, on the other hand, gets fickle winds. Fickle winds is a 6th-level spell that surrounds a spellcaster with wind that essentially makes them immune to arrows and other projectiles that aren't made of magic. It's an answer for the archer's entire approach. Looking at another class comparison, fly lets a spellcaster hang in the air and rain destruction or irritation down on the barbarian from above, and frankly throwing a javelin is not the best use of a barbarian's time. The barbarian needs to rely on someone else to solve the problem for them--there's not a lot they can do.
You can dig into the list of spells and see how many different solutions there are in the spell list--a hard thing for a martial to compete with. And seeing as spell lists are known to expand over time (and with publications), the problem usually gets worse later in a game's lifecycle. It's a hard thing to deal with. Damage, by itself, doesn't do it (although it might reduce the reliance on power attack, removing power attack also has other implications) but this is only one part of their approach, it seems. They have a lot of promising ideas that I can see, like the rebuild of full attacking--so there's a lot of promise--but I don't think this part of it is the important bit for solving the overall problem.
Of course, the dedicated spellcaster players can argue that the wizards deserve to be better late because they're terrible early, and most of the game is played at the levels where they just can't compete. And they're not entirely wrong--the vast majority of the game is played before level 5, and unless your spellcaster has really gotten the hang of their color sprays and glitterdusts and sleep spells, they're just not going to be very good. So it may not be something you want to overfix, which is one of the concerns that's been brought up with respect to second edition.
Oh! And my wife brings up a good point--Starfinder is already testing this out, and it does have a small effect, but the big balancing factor in Starfinder was limiting all of the casters to six levels of spells. Which... means that you don't have any full casters, which does solve the problem, in a way. It also, partially by virtue of the setting, mean that technology can provide a lot of the answers for a martial character that a spellcaster would provide in a more fantasy setting.
More to chew on, I suppose.