Web of trust has been working between humans for over a million years. If we've failed to make computers do it, it's probably just for lack of trying.
To your second point, that might be true in a world where the consequences of making a bad trust decision was some kind of hassle related to changing passwords or reporting your cards stolen. But we seem to be moving towards a world where it lands you in a detention facility or some other dire consequence. I think that sooner or later, users are going to realize that they want that control and will be willing to do the corresponding trust hygiene work. Besides, isn't making that kind of work easy the point of technology? We just need to do better re: making it usable rather than investing in systems we know to be unsafe.
Humans are generally considered to have been around for only ca. 300'000 years.
Also, the interpersonal web of trust is IMHO quite clearly failing in the age of mass media, and not just recently.
> Web of trust has been working between humans for over a million years.
I'm not sure that's really true. Human social organization has, until around 10,000 years ago, been centered on small groups of people where everyone literally knew each other. The ethnographic studies on non-state complex societies generally tends to show a lot of kinship-based networks that developed, and even in state societies that are facilitating long-distance trade, trade patterns and introduction into new areas is heavily reliant on membership of these kinship groups. State societies generally deemphasize these kinship groups, eventually doing away with them like in modern society, but the mechanisms for developing social trust are based on a very centralized development of the legal system--the government essentially enforces that people have to be trustworthy, or they face the wrath of government otherwise.
Essentially, in short, the idea that humans have regularly been trusting people based on asking their close compatriots who they can vouch for doesn't seem to accurately model how trust develops in societies for most of human history--you either have vouching based on direct observation (in small societies), vouching based on identity (larger non-state societies), or centralized authority vouching for people (state societies, including today).