There are, and will continue to be, two sides to currency; the paperwork side, and the "actual" side. The paperwork issues can be managed by exemptions/extensions (medicals, and pilot currency) and flight permits, to allow out of date aircraft to be ferried for maintenance. Here in Canada, pilot medicals have already been given blanket extensions.
The greater issue will happen in the future when things free up, and pilots (and instructors/mentors) who have not flown in a while do whatever it takes to go flying, Will their skills be up to the flight? And then an aircraft which sat for a while, to now be ferried for maintenance, is the aircraft actually fit for even a ferry flight? In the hands of a pilot who's not quite as sharp if something goes bang? Then, the line up in front of the maintenance hangar.
Our society will find a reasonable way to handle the paperwork side for extensions, it'll be up to we pilots to manage the "actuals" of the situation. I think about this every spring, when I fly my first few solo water landings, having not splashed for the preceding six months. It's not like I can find an instructor any more current than I am, the water's been hard for months! I approach the self training with a plan, and extra caution, iteratively getting myself back up to standard. For those pilots who are not subject to a calendar regulatory requirement for a disciplined checkout, it will be necessary that they do an effective self checkout, focusing on emergencies, which seem to be too rusty at the best of times!