Boy howdy there's a lot to pull apart here but ;et's start with your core statement regarding chevron deference. The recent (and wildly stupid, I think but besides the point) Chevron deference ruling says, in summary, that federal agencies have very little latitude in deciding their internal policies where not explicitly defined by congress.

The current administration replaced the head of an agency and had that agency shut itself down. Shutting yourself down is clearly not a power given to any federal agency, so by the very policy you're citing either the judicial or executive branch must act to allow such a move.

Instead, our cheeto in chief decided that those other branches don't actually need to do any of that pesky work and it's a lot easier if everyone just does what he wants.

There's a word for that style of governance.