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Perhaps.

I worked at a company that sold equipment to the military, and almost all of our military sales happened near the end of the year. They wanted their own SKU with guaranteed compatibility for their software, so we charged them extra for it (to be fair, maintaining compatibility did take extra dev work). They never seemed to push back on pricing, unlike our commercial customers who kept clamoring for lower SKUs with a lower cost.

Due to that experience, I highly doubt government agencies are getting anywhere near the best price. And why should they care? It's not like they get a bonus for spending less, but they do risk cuts if they spend less. With no reason beyond obligation to keep costs down, I could absolutely believe each agency could cut about 10% by just being more careful about expenses, some more, some less. With yearly spending of ~$7T, $500B is actually rounding down from that estimate.

It's not necessarily because of expensive toilets, but I do know companies overcharge the government because they can. We did it to an extent, and I think we were one of the better actors because my boss's (the CEO) dream has always been to supply our military, and that's basically the entire reason he created the company (we only sold commercially when military sales dried up due to spending cuts in that dept). We later hired a vet just to get our foot back in the door despite booming commercial sales.