Really when you think about it, government has a lot to do right now with regulating trust. Think of how much more difficult trust between businesses would be if contracts didn't have the force of law? If disputes couldn't be settled in the courts?
I don't want a relationship with the police department, the fire department and I don't see a purpose for the government to regulate phones.
Then there is also the issue that contracts can be voided if the government decides to.
The other, perhaps more important, role is in creating and enforcing standards. (This role might emerge naturally from the results of research.) There must be a defined set of features that anyone providing a "trust network client" has to implement. Preferably such standards would include a provision that requires providers to let users package up their "trust data" and take it to another provider, with a guarantee that the original provider would not maintain it. (After all, you might decide that you don't trust your provider!) Otherwise, it will be the same old story: every private entity in the game will want to control their users' data, and prevent them from going elsewhere. Any moderately successful trust network will be incompatible with the others, and even those that become popular will live and die with the entities behind them.
Imagine if the Internet had been built like that.
But at first glance the thought of the government telling me whom to trust gives me the creeps, too.