I mostly agree with your statement and your issue with companies wishing to eliminate the QA budget (never a good idea).
But I question this bit: "QA Requires a pretty different mindset, one which developers lack entirely."
I don't think that's true. I've done both roles, successfully, at various times. The key, I've found, is that a developer can't test their own work. Developers of a project should also not be put in charge of testing each-others' work if they are working in close capacities. A QA strategy that begins and ends with "test your own stuff", "code/peer reviews" and "write unit tests" is going to reach a quality cliff as the complexity of the software increases. You can get away with it, sometimes, but it doesn't scale.
I'm not sure what the cause of this is, or if it can be improved (it can, but can it be completed eliminated?). It's a similar phenomenon to proof-reading your own work. You mentally add words that aren't there. You follow happy-paths in your software because you know what they are; you don't "misuse" your UI enough[0].
[0] One I think of often was when I wrote a UI for a desk conferencing device. I tested every aspect of it and it was returned to me shortly thereafter when the QA guy joined/exited about 15 "on demand" meetings as rapidly as possible throwing the UI into a state that couldn't be recovered from without rebooting the device.