Well, here are my insights then for why I like rules-lite old school games. These are all my opinions of course, so take them with a grain of salt.
A lot of the appeal for me is the lack of the miniatures rules. Sure, you can use miniatures, but there isn't a guy (the rules) over your shoulder the whole time telling you what the rules say. Your players aren't also discussing how miniatures work either, which I always thought was rather meta-gamey. You can ignore miniatures in newer versions of D&D, but it is a whole lot easier to add in miniatures if you like them, than to remove them (and attacks of opportunity) from the game. Some D20 incarnations have done just that, and those are interesting too, but in different ways.Â
I have about 30 or more pounds of old Ral Partha and Reaper metal miniatures, but I only use them when things get crazy with lots of people doing lots of things. It's also fun to have a miniature that isn't a miniature (like using Monopoly peices)... hehe. But I digress. It is nice to not have to worry about lugging around all of my metal to GASP. Â
There isn't as much talk about what your character will be at 20th level, and what prestige classes they are going to take on the way. I had a lot of games interrupted because people would discuss things that would only happen if the campaign actually lasted that long, if they put ranks in such and such skill, and if they did some other random thing to be allowed for it. I understand why people did this, but it was annoying from where I sat. I think I also had a higher proportion of players that did this than the standard game, so I might be biased. Okay, I'm biased.Â
 I like that the main things that affect your character, are the deeds they perform, the NPCs they interact with, and the items and special abilities they acquire through play.
I like that the power level is more in line with Swords & Sorcery, than high fantasy. It is possible to have a more gritty game especially if magic items are rare. There isn't also a methodology for how much GP a high level character is worth, because who can say at what rate you will acquire such things? It depends on the individual game, the setting, etc. I like the whole zero to hero thing, and it is refreshing to be able to whip up a character pretty quickly, and get them into the game.
I like old school games, because they have a different feel, and are a different gaming experience than most of the games I've played in the last 10 years or so. Sure, I might get tired of Labyrinth Lord eventually, and want to run something else, but for now it is a lot of fun with low stress. The warning signs of GM Burnout that I've had in the past have been nonexistent, and that's awesome. GMs burn out for many reasons, and some may burnout because the rules-lite nature of the games makes them rule on the fly a lot, but I'm that kind of GM, and the random tables that littler the Old School Blogosphere make these sorts of things fun, and interesting.
Here is an example of a fun little random table that I'm talking about:
http://beyondtheblackgate.blogspot.com/2010/12/random-table-weird-things-in-rooms.htmlLow prep time is another big deal for me, and I can even do it randomly (which is fun, because I am surprised too with what comes up). Random wandering monsters are fun, because I don't know what will be around the next bend, and I didn't have to plan for it either. I have the monster stats, and I can wing things depending on what the players do.
I like that monsters aren't always flesh to be killed. If you roll for a reaction (on a table) a monster can be friendly, or not chase them when they run away, or not attack. I was surprised to see that, and I think it's awesome, because again, I'm not sure what the monster will do if I use that little table.Â
 I like that I'm just as surprised with what is around the next bend, or what the monster will do, as they players are. Not everyone uses these rules, but they are in there, and I think they are a gem.
Roleplaying vs. rollplaying is another area where I think old school RPGs shine. You can barter with the GM, and come up with a reason why you would be good at something. It's give and take, and it is awesome to see players come up with awesome ideas on the fly themselves. A GM can even leave this up to chance, and let the players roll it if he wants to leave it up to fate. Sure, you can role-play in every game, but it is in my experience that when you have less on your character sheet that you have to roleplaying through things, because you don't have X skill that you can roll instead.
That being said, I generally let people role-play first, and if it makes sense to the NPC, I won't even require a roll, it just happens. I only really require a roll, when it is a situation that hasn't been explained well by the player role-playing the PC. Again, these are just the ways I do things, and other people do them differently. I like that every game has a unique feel, I like house rules, and I like games that let GMs make rulings vs. having lots of rules to memorize and keep track of.
This is getting long winded. I often say I'm an old school convert, because I never played them back when they were popular. The nature of how the games play was something that I stumbled across, and unexpectedly really enjoyed (I was super burned out on traditional fantasy for awhile).
These above are some reasons why I'm having a lot of fun playing these types of games. They aren't for everyone, but I really don't care about that. I play and run them, because I like them. As long as I can get players, and they are having fun, I'll keep running them. I'll see what the future holds, and hopefully have a crapload of fun along the way. Even if I can't find face to face games, I can go to the game forums and play games there.
I think it all boils down to preference, and if you don't get why someone likes a game, maybe that game isn't for you. I don't think games are one size fits all, especially when there are so many of them out there. Play a lot of games, in a lot of settings, and see what you think rules, and what you never want to play again. Jason, I don't think you will ever like old school games with a GM, and that's cool (you don't have to like them). You may be coming from a place, that I will never understand, because many of your complaints about these types of games, I think are strengths.
It's late, I don't know what else to type, so this will have to do... hehe.