One possible benefit of more accurate reporting of broadband coverage might be more chance of somebody providing coverage to those who don't have it. An area with no existing competition might be more attractive to a provider who is considering serving that area. In my area, for example, a provider who looks at the false maps created with my tax dollars might assume that they would have a hard time convincing users to switch from cable. In fact, customers don't have cable and might happily jump at any option that was offered.
Whether or not this is worthy of taxpayer dollars may be a matter of opinion, which may depend on whether or not you already have broadband coverage and don't care if anybody else does, or whether you're one of those on the wrong side of the digital divide. There are many in government (state, local, and federal) who feel that reliable broadband access for all is a plus for economic development, and that efforts to make that happen are worthwhile. Unfortunately, they're currently doing it in such a half-assed manner that their efforts may be worse than nothing at all.