No.

> Is something like this possible?

Maybe.

> where people have to show "proof of work" in order to have their comments count or rank higher?

This would be counter-productive. You're asking whether its a good idea to remove a persons choice to choose what opinion they should believe in.

It's true that it's easier to criticize an idea when you are not personally involved, but to reduce any thoughts you don't agree with to "trolls and armchair opinionators" is incorrect.

There is simply no way to determine if the person giving advise is an expert in that domain, its one of the advantages of anonymity.

Furthermore, anonymity allows one to step out of the situation and see the bigger picture. For example if a founder was doing something that in an extreme situation could expose users to unforeseeable risks (unforeseeable for the founder), which often happens in the hopes of huge monetary gains.

Also, we already have an option to up/down vote, and if someone says something that is too extreme, not-credible or troll-like we the HN users can vote it down into oblivion.

No reason to deliberately promote cognitive dissonance.