The basis of the PGP/GPG approach is in-person key signing. It can only work if you're willing to authenticate somebody's identity with them face-to-face (keep in mind that publishing your public key online is currently only possible because of CAs). The web of trust model is an improvement to this, because it allows you to choose people that you trust to also perform this ritual properly. But to say all you need to do it figure out how to scale this up is a flawed premise.
The PKI you choose for the internet needs to work for all internet users. The web of trust model only works for highly motivated and technically competent users, and even then, such a user cannot possibly authenticate all of the identities they need to for typical internet use. They end up with a small group of people they can communicate with more securely. They aren't heading off the google HQ to sign their TLS keys, and if they discover a new web service they want to use, they're not going to hold off on using it until a proper key signing ceremony can take place.
Such a system is not fit for the purpose of securing internet communication, and it's not fit for use amongst the majority of web users. Your options for improving those shortcomings is to either create a system that can easily be gamed, by requiring users to trust some sort of community consensus, or to establish trusted authorities (which is just reinventing CAs, and probably in a way that's worse than the current CA system).
The web of trust model simply cannot work for this purpose, there's currently no plausible approach for improving it, and it's not obvious that such an approach is even possible.