This would make fewer people willing to play command roles, which is a problem because we already frequently have shifts where command jobs go unfilled.
It would also negatively impact other station jobs, like IAA/NTR, who would have less problems to uncover (ie: less of a job to do).
It would also negatively impact the antags themselves, since if everyone trusts heads for OOC reasons... you'd probably end up seeing the heads get armed every shift, and function as de-facto security within their departments.
All of this seems like a formula for a less fun game.
Yes, head jobs are powerful, both as antags, and normally. That's one of the benefits they get for taking on the stress of management responsibilities.