I don't think it's that easy to game LinkedIn accounts. Faking the account age and number of connections is non-trivial, for example.

I don't think it would limit the high quality participation, at least not by very much, and that could be mitigated. Maybe users that do not link their accounts could still comment but not vote?

There would definitely be some trade-offs but the current wholesale domination of corporations on HN is a huge trade-off in one direction as well. It seems a very high price to pay IMHO.