What would you replace it with that doesn't have the same weaknesses? DNS already has a robust distribution model (as long as most TTLs are set reasonably high). Its main weaknesses are trust (in the crypto sense, i.e. that lookups are reliably authenticated) and policy (it should be inconceivable that any person or agency could tamper with an established domain name; after all, who fights crime by erasing a suspect's name?). I agree that the current system is being mismanaged, but transferring authority to another entity doesn't necessarily address the inherent weaknesses.
BTW, I'm with you 100% on the madness of TLDs. Sure, reserve some for specific uses, but there's no reason you shouldn't be able to register an arbitrary string as a TLD, and do it cheaply (except you have to solve the problem of domain squatting).
A decentralized/p2p model would help. You could think of a system in which you register a domain associated to a GPG key and you need the key to take it down or change DNS record. This way you get the cloud resolving addresses and you avoid the obvious risk of DNS hijack.
What about the squatters who would make their own keys in the initial rush? There would have to be a central authority to bootstrap this. After the initial bootstrap, the free market could take over. (I'd trust Google or Amazon with this, especially if they knew users could switch over to a competitor if they were P.O.'d)
BTW, I'm with you 100% on the madness of TLDs. Sure, reserve some for specific uses, but there's no reason you shouldn't be able to register an arbitrary string as a TLD, and do it cheaply (except you have to solve the problem of domain squatting).