The General Concept
As far as the general concept is concerned, I would love to play in or run a game like this. I've thought about it a lot, and I'm a big fan of low magic. What has always stopped me from ever moving forward on it is the tendency Ken mentions toward players wanting more builds, more options, etc. In a nut shell I've always feared other players would balk at the proposal and that I simply wouldn't get enough players to run a game. That said, though, I tend toward minimalism so this type of game is something that has a lot (and I mean a lot) of appeal for me.
To be honest, I've even been tempted to run a game with Searchers of the Unknown (SotU) just to see how it works – this is about as minimalist as it gets. One class, and PCs have a single stat line like a monster entry. You pick armor and a limited number of weapons. Action success is heavily influenced by the armor you pick. Most things other than fighting (climbing, jumping, swimming, moving stealthily, etc.) are impeded by armor. So the heavier your armor, the better you'll be in a fight, but the worse you'll be at other things. Armor also modifies your initiative roll, so heavy armor means generally striking last. Extremely simple, but the choices you do make are very meaningful.
"Not much character class choice."
This is really the big challenge Ken mentions that has always stopped me proposing a truly minimalist game to any group I've played with. One thing I've considered in my own ruminations on the topic is running a game using just fighters and thieves in conjunction with something the "130 Classes?" in Dyson's Dodecahedron Vol. 1 No. 7. Dyson gives each class a list of something like twelve one-line subclasses (essentially one single skill or feat that makes fighter A different from fighter B, along the lines of "Archer: gain +1 to hit and damage with ranged weapons"). This could mitigate the "lack of options" issue a bit while still maintaining the desired streamlined nature of the game through its simplicity.
"YIKES! No healing spells!"
Hit point recovery could involve a rule like the one in SotU: recover all lost HP after each combat (one might have to exclude trap damage though, since otherwise traps become pointless unless they can kill you outright). Short and sweet. If you want things to be deadlier, maybe recover ½ HP lost after each combat. Or maybe you just give PCs more HP to start with, and then don't do anything. You could still have PCs finding potions and pools and the like in the dungeon to heal up. If you put persistent, static healing pools and fountains and such into the dungeon, these healing locations would take on extreme tactical importance for the PCs too (see below), as the locations would likely become staging areas, rally points, and rest zones.
"Magic items become highly prized;"
"Highlight the sense of danger and weirdness with regards to the dungeon."
I have always thought that the rarer magic is the more special and wondrous it becomes, so I agree with Ken's idea that "magic items become more prized." The same applies to the weirdness of the dungeon. Only things that are rare are special. The mundane is mundane because it is common. The value, wonder and weirdness of anything diminishes in proportion to how common it is.
"Lack of magic reduces the party's tactical options and abilities;"
"Focus the players to find different and creative solutions to challenges poised by having such limited options;"
"Focus play on exploration, rather than tactical combat."
I don't know that the loss of tactical options would actually be too much of an issue. I suspect the limitations are just as likely to promote tactical creativity of a different sort. The GM probably would need to be extra sure to add more terrain features to the dungeon which players can try to exploit for tactical advantage – high ground, low ground, obstacles, and so forth. Maybe even movable objects that can be used in combat, employed to build barricades, etc. But pushing a bunch of boulders over on your enemy from a high cliff is just as tactical as choosing a specific attack from a menu of options in the rule book, or using spell X or Y in a given situation. The former is just not "rules-based." But it's not any less tactical.
In terms of tactical decision-making specifically related to magic, a GM could borrow the rule from SotU allowing all characters (i.e. our fighters and thieves) the ability to use scrolls when they find them. This would allow magic and its tactical options into the game while still limiting the magic to keep it special and prized, since the GM controls just how many scrolls are out there floating around in the world. And the choice to use/not use that scroll would become even more significant. Since there is no getting that spell back the next day, and there's no knowing when you'll find another scroll, you really need to pick and choose when you're going to fire off the spell on that scroll.
"It could just really suck and be boring."
This is the least of my worries, since I don't think this is really a function of the rules at all. One of the reasons why I gravitate toward the simplest rules I can get away with is that I find 100% of the fun of the games I've been in has come from the creative energy the GM and players put into it. Two cases in point, using multiple rules sets in the same campaign. I've played in Ken's Montporte campaign using both Blood & Treasure and D&D 5e. I've played in Rob Conley's Majestic Wilderlands using GURPS, Swords & Wizardry, Rob's own Fate/Fudge-based rules, and D&D 5e. I had the same fun in both those campaigns regardless of the rules. Rules choice in no way increased the fun factor. What mattered was the world and adventures Ken and Rob created, and the creativity with which the group of players approached them. Which reinforces my high opinion of low-complexity rules. If I have the same fun playing a rules-lite game as I have playing a rules-heavy game, what am I gaining by spending the extra out-of-game time learning all the ins and outs of the rules-heavy game? I've got limited spare time and I'm not really interested in spending it on learning complex rules that provide me no reward at all in terms of fun factor. Rules-lite only means the game "sucks" and is "boring" if the GM and players aren't bringing creativity and energy to the table. Admittedly I've been lucky in this respect, in terms of the groups I've played with either by post or in real time on line.
My Bottom Line
In short, this is totally a kind of game I'd want to have a go either playing or running. There might be factors I can't foresee that ultimately cause it to implode, but it's something I'd totally love to try.