Capacity study? Hahaha Like they're going to go to the schools and someone there will "know" how much internet they need. They can't even go to the schools and get a good estimate of how many students they expect to be attending in 10 years, almost all the schools in the US are reactive to that sort of thing, they build new ones when the old ones are either so broken down that they can't fix them or they are over capacity. If you go to the schools you get one of two things: 1) a tiny internet straw that 2000 kids share and it's useless or 2) an OC48 to a tier one peer that 163 kids and teachers use for email.
There is something more fundamental, there were probably schools that had nothing close to reasonable internet access. (Likely a lot of them were in places where they can't get great internet at home either.) The masses were fed up with it, especially as they thought their kids were being left behind so they beat on their representatives and they just got a blob of cash to fix it, costs be damned. You think it was going to make the parents happy when they announce that it's going to take 7 years to get DSL to their child's school?
It's a monster of our own creation. No idea how you solve it... the people that doll out the money have no idea how to do the work or how to estimate if an estimate is good or not; they're just too far away it and the public's memory is too short term.
They probably did open an RFP to multiple bidders.. That's just game theory though, you think the bidders want to leave money on the table? Every where I've seen government bids produced, they increase the costs.