Tor never claimed resiliency against large-scale traffic correlation attacks. Anyone who can look at a sufficient portion of all internet traffic has a good chance of deanonymizing TOR users. The Snowden revelations could lead one to believe that the US is sniffing enough traffic to make this viable, but it's anyone's guess if they collect and synchronize enough data to make deanonymization of TOR users viable.
I2P always looked more promising to me, and more open about its threat model [1] and potential mitigations. But it's not built for browsing the open internet, so it has a somewhat different niche.
Running an exit relay from home would be a very bad idea, and if your IP frequently changes you might not be picked as guard relay. But I don't see why you couldn't run a middle relay from home, as long as you don't have a traffic cap.
You can run an exit relay from home, at least in the US. There are some ISPs (mostly on the East coast, afaict) that may not help you, but most of them seem to understand how the laws work.
Tor was originally written by US intel agencies specifically to provide cover for spies. The release of the software to the public was specifically to provide plausible deniability for those spies. So there's always going to be some level of control and knowledge the US has about the network.
If your threat model is anything weaker than a hostile nation state then Tor is still probably good enough to use as a darknet. If you're doing anything illegal over Tor then you probably should be more worried about OPSEC failures or rubber-hose cryptanalysis.
Are you sure it was supposed to provide "cover for spies"? AFAIK onion routing was an invention of the US Naval Research Laboratories and was public from the beginning. If you want "spies" to use it, you don't want them connecting to known gateways. High anonymity (simplex) is why number stations are still a thing.
They're still a thing as recently as a year or two ago when I looked into it. They're "perfect" in that the receiver can't be identified from the message or its channel (other than catching him with his radio), and that the message cannot be reversed (encoded w/ a one time pad). So they're hard to replace.
It's better than Tor in a few ways, in particular how it handles DDOS attacks. I2P is also more focused on facilitating hidden services (eepsites) than being a clearnet proxy.
There's also Yggdrasil, although it doesn't seem particularly concerned about anonymity.
Mesh networks that don't operate as an overlay network could in theory be pretty effective to avoid large-scale traffic correlation attacks. If we assume that the US has effective control over the whole backbone network, and enough control inside the network of most commercial available ISP's, then there isn't much mixing networks can do. An adversary can always observe, inject, throttle, speed up, block and otherwise disturb the network flow in order to determine who is talking to whom.
I hope not. Tor being used for whistleblowing and censorship circumvention is one thing, but the onion network is pure anarchy and probably the worst case scenario of what the internet could become.
It is useful as a free-for-all outside of censorship.
You probably don't want an area free from censorship most people don't. I browse with safe images enabled when searching google images. Once in awhile I'll open it up and see a world that didn't exist before. I don't think that world should be removed even if I rarely visit.
I2P always looked more promising to me, and more open about its threat model [1] and potential mitigations. But it's not built for browsing the open internet, so it has a somewhat different niche.
1: https://geti2p.net/en/docs/how/threat-model