I don't think recent democrat Presidents share your view here.

Seems unlikely that they didn't. After all, none of them initiated any mass firings of the non-appointed agency staff. They pretty much filled positions as they came vacant, and had to live with whatever staff they inherited from their predecessors.

The problem is the democrats never follow the "rules".

They do follow the "rules." But the "rules" are intended to preserve continuity in Federal policy, not abrupt changes in the aftermath of an election. The "rules" are:

1) Congress creates, funds, and oversees all the agencies - so most of the agencies are locked into doing what Congress wanted them to do when they were created, even if the President doesn't currently share those priorities.
2) Congress adopted the Civil Service acts, which make the overwhelming majority of federal employees long-term professionals that tend to align with the missions of their agencies.
3) Congress passed the Administrative Procedure Act, which requires agencies (and therefore the Executive) to show their work and provide notice and comment periods prior to any major changes in federal policy.

All of those combine to make the federal government very much not operate like the type of closely-held family private corporation that Trump is from, when the entire organization has to be very much responsive to whatever the CEO directs at that time.

BTW USAID was initiated...by executive order.

And later codified into a formal agency...by Act of Congress:

https://uscode.house.gov/view.xhtml?path=/prelim@t...

Which is why DJT can't just "shut it down," despite his Administration's claim they would do that. It doesn't matter how it started, it matters what the legal status of it is today.