Other levels of gov have funding issues, but not federal. In fact, big appropriation bills often create these mega-procurements that companies like BAH latch on to.
Government's ability to attract people who could execute a project like this requires different compensation and career incentives. Base pay is capped at <$150k for the highest GS level at the highest step. There's also no real potential for bonuses or equity.
Beyond pay, government careers fundamentally optimize for low-risk decision-making. The goal is to not get fired over 20 years so that you can retire with a pension. This is why contractors like BAH gets hired: you, as a government program manager, don't get fired for going with a brand name even if they fail. If you hire some unknown development firm with great tech skills and they fail, you get canned.
There's also a lack of bold leadership and urgency that is customer-experience focused. Healtchare.gov benefitted from some amazing engineers, but the true catalyst for its comeback was that Obama realized it was a do-or-die initiative for his administration. His team moved heaven-and-earth to steamroll entrenched vendors, recruit talent, and hold people accountable.
Leadership and talent are what make the difference.