Lol the Democrats never “rested their case,” far from it.
There were plenty of outstanding subpoenas that have either been blocked by flimsy/waived/non-existent claims of executive privilege or else totally ignored.
The nearest precedent for this is when the Supreme Court unanimously overruled the Nixon Administration’s claims of Executive Privilege in regard to the Watergate tapes.
Given that unfavorable precedent, the Trump Administration should not need a Supreme Court order to comply with their constitutional duties. Then again Trump violated his oath of office already (Art. I), so it is not surprising he would violate it again to cover it up (Art. II).
In no other trial would a Defendant be able to block the prosecution from even collecting evidence like this.
Anyway all this information will come out eventually through leaks, further House subpoenas, or certainly by the time the next Democratic President takes office at which point all the blocked docs will be released and everyone else will be finally forced to testify.
Trump and the GOP have only bought themselves time. When the inevitable reckoning comes, it will be much worse for them, because... it’s not the crime, it’s the cover-up.