I would doubt Gates's number because I have never been in a company that had 15% or less waste. e.g I don't think you could find a tech company out there that couldn't reduce its AWS bill by 15% without any service degradation, but it's just not a priority.

But the meaning of "waste" is highly subjective so some people wouldn't count that type of inefficiency as "waste". It may take a lot of resources to follow the process that the government mandates or use the ancient technology that it uses, and if the government efficiently follows the process with the existing tech, then it's not "wasteful." But I would call the process itself and the failure to upgrade the tech waste.

As for corruption vs bureaucratic inefficiency, why should I favor one over the other except by cost comparison? If the government pays $100 million to build a road that really costs $50 million because the contractor is owned by the governors cousin, that's a lot better for me than paying $200 million for the same road because the bureaucratic process to keep the governors cousin from unfairly getting the contract costs $150 million. And that's not even getting into the fact that the bureaucratic path also costs more in terms of time.

IMO the process is just as much graft as the nepotism. All those lawyers and consultants and government employees that consume the $150 million are just as much the recipients of ill gotten gains as the governor's cousin. I recognize that this can't be eliminated, so I simply would choose whichever one was cheaper. And in the US I think we are in a situation where the bureaucracy consumes much more than would be taken by corruption. China is quite corrupt and yet their government gets a lot more done for a lot less money, and in a lot less time than ours does.