"This profile doesn't have anything on it. Give us the password for the real profile."

Or even worse, you did give them the real password, but because your phone supports the feature and your profile is kind of barren, they don't believe you. Now you are in a very bad lose-lose situation.

As a retro gamer myself, my opinion is that going for original hardware and even hardware emulators like the MiSTer only makes sense if you then use a decent CRT as the display.

Using an LCD adds unacceptable delays, even if you get a very expensive upscaler (though they do reduce it a lot, but not entirely) at which point you lose all of the advantage of using original hardware or an expensive hardware emulator.

If you're going to play on an LCD, just use a PC with the Duckstation, Mesen, Dolphin, MAME, Final Burn Neo, and PCSX2 emulators, which will get you all of the popular retro systems emulated more than good enough. Retroarch can be added if you need some of the other systems.

Note also that if you play on a sufficiently high-res and high-refresh monitor, there are some really convincing CRT simulation shaders, including realistic phosphor delay.

There's two exceptions to the above: N64 emulation is still not perfect, and if you want to play something more obscure, the available emulators may just not be good enough, such as for example the CDi and 3DO. In those cases, real hardware is better even if you don't have a CRT.

Edit: Oh and of course handhelds are honestly best played in handheld form factor. Either get original hardware, or one of the million small handheld emulation devices, all these systems are emulated near perfectly.