I am sure that Nintendo is using FPGA for internal R&D, so they have people capable of writing cores for FPGA. Add to that the fact that Nintendo has all the schematics and detailed information about the original hardware and designs.
Yes, a FPGA would have been work, but not lots of work for them. And we are speaking of 8 and 16 bit hardware, that is very small and limited hardware.
Besides that: Windows can run on a Raspberry PI, so maybe the emulator on Windows used by Nintendo is already using that. Who knows?
They could replace all the parts in a SNES or NES with components indefinitely, because inside are either off the shelf components or specifically made components made after schematics from Nintendo. So even if nobody makes such parts anymore at the moment there is nothing (but time and money) that would stop Nintendo to order new parts based on their schematics.
Most issues with old consoles can even be fixed by hobbyists and if they can't that's because they don't have access to the needed information to create new versions of the tailor made components.
So there should be no issue for Nintendo to supply their museum with replicas forever. Yes it would cost way more money then using Emulators, but it would be way more appropriate for their own museum. But no they have chosen the lazy route.