It’s wizardry Simon!
Not at SketchUp now, but I wonder if scaling the polygon might work in the same way too.
NO.it is “destroying” the Polygon to Curve
Definitely SU dark arts!
So the answer to the OP is don’t use the Rectangle tool, use the Polygon tool.
This is what you get from someone clever enough to replace their nose with a stein, I guess!
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Again, just as secret info 
, among my many unfinished and unreleased plugins, there is one (similar as a combination of native Rectangle and Polygon tool) with which I draw a rectangle with a center like this above … with two clicks.
Using two inferences from two adjacent sides is quick.
Almost as quick is drawing only one diagonal. Then, you can infer its center which is, of course, the center or the rectangle. Delete this diagonal when done.
The benefit is that you can use the cardinal points, even when pushpulled. No need for scaling!
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