>I guess the primary purpose of the audit is to make all the numbers add up, and maybe that can inform cost-saving decisions down the road

That's right - the, not unreasonable basis, is that you can't make informed decisions about whether you're getting good value for money, or how to change allocations, unless you've transparency into what that money actually does.

It's approximately the same reason why financial statements and their audits are relevant in the private sector - just substitute "investors" for the "the public, with Congress as proxy".