I think when people say they dislike the "Top" lists, what they're really saying is "I'm already fairly well known and could easily get editorial featuring if we moved to an editorial-only model." This type of system would actually be much worse for indie developers, I think, as they would have to have a connection somewhere to have any hope of getting featured (much like you need to know someone to get onto Steam). Most of us dont have $20-$40k to buy our way onto a top list, but knowing that we could without having to have a publisher or hookup at Apple is a great equalizer.
New and Notable is actually a very good example of Apple showing pretty decent (and even handed) editorial review. By and large, anybody putting something with a reasonable amount of care and attention, gets some exposure there in their category.
I'm wondering if the Appstore has gotten large enough that an independent review site/app could make money? And, I mean a honest to goodness review site - not these scammy "pay to play" apps that have been plaguing the app store recently.
Also - if you could just survey a list of 10,000 honest users - that would be pretty good as well.
The sad thing, is some amazing apps on the store (for example, gymbuddy, one of the great weight lifting apps) have languished because only those people who actually use the app seriously would appreciate how much better it is than the competition. I.E. Can you imagine what the WeightLifting App Section in the AppStore would like if you surveyed a 100 lifters who had tried out a dozen or so apps before deciding on the one they like? Likewise for people who make pastries, check the weather, survey tree's, watch the tides, etc, etc...
No, I'm pretty sure that when people say they dislike the "Top" lists, what they're really saying is pretty much what Marco wrote here.
Editors' picks are always a wild card because you don't know on what basis the picks are happening. But your assertion that they're always about the "connections" you have strikes me as, well, very anecdotal. I have some experience on both the submitting and receiving side of magazines, and generally speaking what gets your story accepted is the quality of your story. People often assume you need "connections" to get into big name markets, but big name markets attract big name authors and that makes the barrier of entry much higher. I have no inside knowledge of Steam, but I suspect that's very likely what goes on there: the more developers want to be on Steam, the harder it will be to be on it.
Of course, Apple already has editors' pick lists which I've heard really do boost app sales significantly; the question is really whether dropping Top 10 lists would flatten the curve further; I suspect the sales would remain vastly overweighted toward the featured apps no matter what, but perhaps if the featured apps were rotated frequently that would help. I rather like one of the other commenters' ideas of keeping the top 10 lists, but just removing apps you've already purchased from them.
The App Store search is pretty bad, as other people have commented. (A lot of people think the changes to the store in iOS 6 made it worse, but it's not like it was good to start with.)
While it may be a problem that top ten rankings can be bought (I haven't seen any evidence that it is a problem), without those organic downloads from the top of the charts it would be much much harder to build a growth business out of the app store. Turning off the top rankings seems like it would prevent there from ever being another Angry Birds or Instagram... discovery is too hard otherwise.
Even an editor ranking is ephemeral. Say you're right and the cream rises to the top--how long would a feature last? A week? Two weeks? Maybe a couple hundred thousand free downloads?
I don't know what the organic/non ratio is at most companies relying on paid installs, but my gut would say it's somewhere on the order of 1:1 or better. If you remove the organic installs, CPIs would essentially double overnight and most of these businesses would no longer be able to sustain themselves.
