Who's ignoring it? Once the problem is identified by someone, you fix it and move on. This already happens.
$1,300 coffee cups: https://www.airforcetimes.com/news/your-air-force/2018/10/22... Audit of C-17 Spare Parts: https://www.dodig.mil/In-the-Spotlight/Article/3948604/press...
See also, the myth of the $600 hammer: https://www.govexec.com/federal-news/1998/12/the-myth-of-the...
Trashing whole departments/agencies first and then trying to find all of the 'waste' amongst the wreckage creates more work in the long run when you have to rebuild all of the processes and try to reclaim some portion of the institutional knowledge that got flushed down the toilet for no reason.
I'm sure I'm missing something, I'm no expert by a long shot, but government spending isn't a secret. Budgets get approved by congress and spent by the executive out in the open. Maybe someone interested in curtailing waste could start by auditing budgets? Making sure that the money allocated got spent where it should have and that the budgets weren't padded with unnecessary spending? But that takes a lot of time, effort, and energy, is kind of boring, and wouldn't generate dozens of headlines every day.
It's not an either/or situation. You can have responsible spending and also services to benefit everyone. Cutting me a check to give me back some of the money I've paid into the system doesn't make a whole lot of sense if you only got the money by destroying the CDC or whatever.
It would be kind of like the gas company tearing my house down because my windows aren't insulated and then giving me a couple hundred bucks because they technically eliminated the source of the wasted energy