"Instead of actually going with the lowest bidder .. " In many states, it's law that they must go with the lowest bidder. This often causes problems because that lowest bidder delivers shoddy work that leads to eventual cost overruns--going with the "best value" instead of "lowest price" would reward companies that could meet both cost AND quality expectations. It'd also more closely reflect private sector considerations if those laws were changed; a private company can spend more for higher quality and get the long-term benefit of that quality deliverable, and that's a trade-off and decision that's simply taken away from state/local procurement professionals.
State and local procurement tends to run pretty lean, and tends to be pretty accountable. All this stuff is public record, and local papers will often cull through that stuff looking for juicy nuggets. The relative rarity of public purchasing scandals, at least for state and local folks, tells you that they're probably doing a pretty good job (even with the goofy restrictions like "you must buy from the lowest bidder even if their work is shit").