The problem is deliberate hardware choices. They may be reasonable choices, but if Nintendo wanted to prioritize forever backwards compatibility, we could still have a GameCube-compatible disc drive and GBA and DS compatible catridge slots.
I think being an official product makes it totally different and much more special. Maybe that's silly--but consider how well the NES Mini sold compared to similar unofficial products. (Unfortunately, the NES Mini couldn't read cartridges.)
If it was an official product, it would have to read from the real cartridge or disc. If nothing else, Nintendo does not have the legal right to redistribute games made by third parties.
This is fair, although I do think the choice was reasonable. Disc drives are an expensive part, and consider how much space a cartridge slot would have used on the 3DS...
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I have long had a total fantasy in this vein... what Nintendo could have done is release add-on hardware to read old media. Imagine a hybrid mini-disc and cartridge reader which connects to the Wii U via USB, and a Gameboy cartridge reader which connects to the 3DS via... uh, possibly NFC, Gameboy games are small and the games could be read once and cached to internal storage.
You could use this to add backwards compatibility all the way back to the NES and Gameboy! Games from consoles two generations back could have been run natively, everything older could have been trivially software emulated.
I don't think such a product would have substantially interfered with Virtual Console sales, it would have been too niche. Probably too niche to make sense in real life... but in my fantasy, the goal would have been PR. It would cement the idea that buying a Nintendo game is an investment which Nintendo will support long-term; whether a large number of people make use of that ability is irrelevant.