Is there an organization trying to promote a parallel branch of the web —but an authentic one— where user would surf with their true identities? (Individual identities will be checked with the same importance they are now for money transaction).
That parallel web would look like a google where only identified users would be able to login. It would not obviously replace its anonymous version (the current web) but offer a complementary usage. People could choose to surf on the current web but will have to prove and show their true identity to access the "transparent web" (let's say Tweb). This Tweb will be reserved to people looking for an authentic web experience.
Ideally a same website could be accessible from both webs to gain as much benefit from the anonymous web (e.g. to keep the freedom to talk about controversial topics) and the transparent one (cf. the benefit below). The webmaster of this website might be interested to offer different services according to the type of connection chosen. This duo system would establish a healthy separation between opinion (that could be anonymous) and behavior. Enabling anonymous connection for opinions will help to avoid the conformism tendency that will result from a unique transparency network.
Some advantages of this transparent web: It would not solve all the problems but reputation and transparency should bring more self-control and responsibility. This should, by extension, create more trust but also respect, more empathetic behaviors and all these things needed to build real human interactions and real communities. Trust and reputation might also increase resource sharing and cooperation: imagine a web where you could lend or give money to anybody simply based on his reputation. This transparency network would favor pro-social skills (such as honesty or integrity) and discourage the lack of it. It would be a web without captcha, spam, and maybe even password where you could quickly evaluate who you are dealing with.
1 As AJ Henderson mentioned, a hybrid platform that would allow both: verified + unverified user on the same service would not be interesting. The idea is to allow only verified users in a specific part (where anonymous will be forbidden), and tolerate anonymous login only for the other part that would benefit for it. The "opinion network", is needed to avoid conformism bias).
2 The main point of this would not be to create secure connection (it already exists). It's not either to build more trust and transparency between the user and the webmaster (even if it will be a happy side effect). The main goal would be to create trust between the users, to emulate real community dynamic (through a verified identity and transparency between user)