Cable that you'd plug in where? The power port? The SD or game slot? There's no way to plug a device into a 3DS like you're thinking, they haven't had such ports on Nintendo handhelds since the GBA. IR or wifi are the only ways to do that on 3DS, and wifi would be overkill for how little data is transfered in Amiibo usage.
BTW, the Circle Pad Pro also uses IR to transmit to the 3DS. Which now that I think about it, might be part of the reason why, despite supporting the New's nipple stick, Smash Bros doesn't support the CPP. I know they say Smash pushes the 3DS too hard for CPP's overhead to work, but they also make a lot more selling Amiibos than CPP's, so I wouldn't be surprised if they didn't try to hard to get CPP working, knowing they'd need to keep the IR sensor free for the Amiibo reader. Just wild conjecture on my part, no proof of any kind.