Those applicants perceived as less desirable (for whatever reason) need to hedge their bets by applying as widely and enthusiastically as possible, but this would make it more difficult for them to do that convincingly.

Given that those who are perceived as desirable hires already have a lot going for them, can it really be a good idea to give their chances of getting what they want an additional boost, at the expense of those who lack the advantages they enjoy?

On the other hand, there is prima facie a potential benefit to departments, who get more information about who’s really keen on them. But do they really? If I were faced with this system, I wouldn’t necessarily signal the two depts I most wanted to be in; I’d probably signal two of the ones I liked that I thought I had a chance with. Or, perhaps, one such department and one “insurance” department. But once hiring depts know that this sort of thing could be going on, the potential to gain significant information from a signal is much reduced. Except in the special case where a very desirable candidate signals a considerably less prestigious institution than you’d expect. (And even then, the mechanism relies on the receiving dept having the humility to realize that the candidate is out of their league!)