That being said, labor markets are very complex and there's lots of strategic maneuvering going on. Given the indeterminacy of much of game theory (i.e., it depends on how you model the scenario), I'm sure you could be right under the proper assumptions.
But to bring it back to the SO example, it's hard to imagine a scenario where giving high ability workers the ability to truthfully signal that high ability hurts. Low ability workers can be hurt i.e., either I know you're bad from your SO rep, or I start to think "hey - where's your SO profile? you must be bad." In the pre-SO system, the low ability workers were getting an unearned rent (assuming the market existed at all) at the expense of the high ability workers and firms (which is market-killing).