Why would it be horrible? Your IP packets already take a bunch of jumps to get to you. Adding another 5-10 jumps shouldn't be a huge issue, should it?
Maybe someone with more experience in this field can comment, but if you want to replace the last-mile connectivity, I don't think it is going to just be 10 additional hops. I doubt the latency would every be low enough for gaming, voip, and video chat. And the latency might be high enough that browsing the web recreationally would suck so much that you rather not bother. There is still a lot of use cases that would be great: blockchain transactions, text messaging, email, search results, staying up to date with the news (particularly if the device automatically pulls it from subscribed feeds in the background), downloading important software updates, batch downloads of content/media, and perhaps even streaming media if the mesh network can handle the bandwidth. In my view the mesh network technology is good to have to provide basic internet connectivity to people who cannot get it otherwise, so they can keep up to date with news, do business, and communicate with each other. I think the technology applied to WiFi sharing (with regular wired backend) is fantastic to reduce our dependence on the incumbent carriers and their cell networks. But this doesn't replace people's desire for high bandwidth, low latency fiber to the home.
It's not settled that legal liability would attach. There have been some cases about people not securing their wifi connection in their homes, and outsiders using their wifi for evil purposes, and I don't think anyone has gotten in serious trouble for not securing their wifi. It won't be target by government unless it is fairly popular, and once it is, there may be little they can do. Your example of tor for instance is apt. Tor is still going.
I am just saying this legal uncertainty can kill adoption. My example with Tor illustrates this. Very few people care about using the slow Tor network. If people are too scared to be exit nodes in this network because of the legal liability, the internet access in this mesh network is going to be very slow. It doesn't even matter if they win the court cases. The fact that they need to defend themselves in court already raises their costs which they need to pass on to mesh network users with higher fees. People won't bother with the expensive, slow mesh network when they can get a cheaper, faster cell network (not even mentioning wired connections).
Ideally, there would be either overwhelming court precedence or a group to lobby the government and pass laws that makes it clear to people that they won't get harassed for relaying information in a network. That way it ends people's hesitation in participating in this network. But I doubt the government is going to give up the harassment until they get some other way to get the information they want (someone to point a finger to as being guilty for either
unauthorized access to computer systems, aka hacking, or
publishing, whatever that means, information they deem
inappropriate). The government's whole logic behind all of this is IMO so flawed to begin with (I don't want to get started with that), but it is the reality we live with currently.