The FAA's main reason is that they want to be able to physically take your only legal certificate away from you if they suspend or revoke it. In this day of instant database checks, that might seem unnecessary, since an Inspector could check on your medical/airman certificate status instantly via cell phone 24/7, but it's no different in that regard than DL's and cops, where you must have the actual original DL with you when you're driving.
The FAA hasn't updated to the technology of electronic certificates as there is no real need for it. Medicals are still on paper. It would literally take an act of congress to change the format, just as when certificates went from paper to plastic.
Same reason that a digital of your drivers license and inspection sticker won't if you are stopped for a traffic violation.
Must be SSA, because the FAA is perfectly happy with a laminated medical certificate (asked and answered by the Chief Counsel) once it's been signed by AME and the holder. Only exception is the back of a Student Pilot certificate, which must be endorsed by your CFI for solo (each make/model) and solo XC (unless you won't need any further solo endorsements).
I don't think Congress mandated original pilot/medical certificates (that's up to the FAA) but Congress could (if they wanted to) order the FAA to go to (or at least allow) e-certificates. Only problem is Congress would also have to provide funding for a system for that, too, or the FAA could ignore that unfunded mandate (like they ignored the Congressional mandate to put pictures on pilot certificates for lack of funding), and they're a bit short of funds these days for things that aren't going to result in a lot of votes for reelection (this, I think, not being such).
I've seen that happen. OTOH, I've also seen it result in a more in-depth check to see if that was the only issue, whereas if the initial document check had been in order, that would have been the end of the check. YMMV, but I suspect the least painful ramp check happens when the Inspector gets bored quickly by everything checked in the first five minutes being in order.
And I concur entirely with that.
'Zactly. Gives the FAA an out when Congress passes an unfunded mandate.
You're right on the Drivers License, but I recently learned that a digital copy of my auto insurance is promoted by USAA and acceptable in CO, at least according to my friend in Jeffco Sheriffs Dept.