I think museums are actually a perfect application for emulators! Don't get me wrong--nothing beats picking up my childhood Game Boy and playing some Pokémon Blue or Super Mario Land. But in a museum context, exhibits have to be robust, and you'd likely be churning through consoles as they withstand all manner of abuse. More interestingly, emulation can allow you to do things that just aren't possible with real hardware.

Random example off the top of my head: let's say you wanted to have an exhibit where you want to have patrons do Bowser throws as a demonstration of how Super Mario 64 tried a lot of new things (some more successful than others). How would you set this up on original hardware? Let's say you set up the game with 99 lives paused as the player enters a Bowser fight. Sure, this will allows someone who dies to enter a bunch of times, but as soon as someone wins, exits course, or runs out of lives, your exhibit is borked and you'll need a staff member to come and fix it, which will take a not-insignificant amount of time and require game-specific knowledge. But if you use an emulator, you can use save states and set the emulator up to automatically reload a save state pauses at the start of the fight whenever someone leaves. If you use a replica N64 controller they will get a practically indistinguishable experience while also allowing for a much more functional exhibit.

That's a simple example, but the sky's the limit with emulation. I was just looking at a super cool preservation project which translates exclusive mobile features from the Japanese version of Pokémon Crystal into English and also interfaces with replacement server software to allow users to replicate the experience of being able to hook your Game Boy up to a cell phone and access services like trading, battling, and news bulletins. Even if you had all the original hardware, it wouldn't work because the network technologies old phones rely on have long done been sunsetted. But with emulation (and perhaps some trickery with the physical exhibit for immersion) you could set up an exhibit that lets patrons experience this really ahead-of-its-time netplay feature.