That's the kind of thing that sounds simple but requires a little deeper thought to see how frought it is.
One step deeper is that on its own terms this would be seizure of private property. Fine. But, on account of "no external authority has granted them private ownership?" We don't normally accept that all is government by default, unless permission gives us permission to own.
Deeper is the nature of government ownership itself, as it's necessarily realized through executive branch interference. That's what ownership IS, functionally, so this implies presidential control over Supreme Court function.
No, this is a very bad idea.
Court control of court papers is not an anomaly but a simple implication of the independent judiciary.