Issue with corner selection and manual values

Personally, I find the whole idea of the round corner function very confusing. Why is it in so many places but works in different ways?

If I select 4 out of 4 corners, I can see the round corner input box in the Transform panel and in the Control panel, but not in the Properties panel. There, the box is only visible if 3 out of 4 corners are selected.
I don't understand the logic behind this. What is the purpose of the behavior? How does this make life easier for the user of the program?

And what is the idea of showing redundant information on (at least) three different panels;
- Properties - has almost all the functions that Transform has, if you press the three dots under the dimensions, plus some extra.
- Transform - Doesn't really have anything that isn't already under Properties
- Control - Shows a selection of the functions

This is quite confusing. When should I use which of the panels? More importantly, why does the ability to edit all corners disappear when 3 of 4 of them are selected under Properties?

View > Show Corner Widgets does not solve the problem, but Window > Transform works fine, as a workaround, but it means I need to have yet another panel open. Is the Properties panel behavior "by design", me doing it wrong, or could it be a bug?