Is there any point to keeping the CSCE form after the FCC registers the exam/upgrade in its database? I'm trying to go paperless in my old age and if there's no reason not to have the paper copy, into the shredder it goes.
You can shred it.
The only time where such paperwork proved valuable was from the days of "Tech Plus" (passed written element 3A and 5 WPM code). The FCC eventually reverted Tech Plus to Tech licenses. When the code requirement for General was dropped, former Tech Plus licensees could get "automatic" upgrades to General if they could show paper proof of their former status. This was back in the days when paper, not bits, mattered.