My thought was more marketing dollars and shelf space. Carrying 3 consoles, related accessories, and Amiibos takes up a decent chunk of room. Nintendo just has a terrible time matching demand/striking when the iron is hot, even the new 3DS was OOS everywhere around Christmas, and depending on how similar the mini NES hardware is to the 3DS (both ARM based), it frees up components dropping the former.
And if/when the Switch adds its VC, having the mini NES around makes those $5 digital ROMs less attractive.
Otherwise, I agree they're targeting mostly different subsets of Nintendo gamers, the mini NES is more geared more towards the retro set (but I still contend a Pi is a just better all around option).
It's not just carrying 3 consoles, Nintendo is carrying 3 products with different timeframes in mind. The 3DS is only going to stay in production until 2018 or maybe 2019 at the latest (or until the Switch gets enough momentum from both a sales and development standpoint, which it seems to trend towards given that it's selling + it's getting at least one big title per month until July/August). That's why they didn't produce more during the Christmas season, and even if they did, it's still going to take time, so they bit the bullet on the Christmas season. It's hard to blame Nintendo for the 3DS given their intentions to wind the console down. However, Nintendo judging the NES Classic as a Christmas product is inexcusable given the clear demand and the low production of the console. I can understand why Nintendo discontinued it, but they are shooting themselves in the foot for not extending the production beyond simply being a "Christmas gift" product.
Also, I don't see what being similar in hardware has to do with anything. That disregards the clear technological differences of the devices and the demographics they're trying to target. That being said, thats why I don't buy the "NES Mini makes VC less attractive" argument. That's one thing to note, the NES Mini isn't just resonating with Nintendo gamers, it's also resonating with people who used to game before and never really caught onto future consoles like the Nintendo gamers did. It's a nostalgic product that resonates with both the hardcore and casual users. If the NES Mini is targeting the retro/nostalgic people, and the Switch is targeting people that want a new gen console, then why does it matter or rather, why do people assume that it automatically makes the Switch VC irrelevant? Those same NES mini customers aren't likely to own a Switch so they don't overlap to the point of concern. Not to mention, there are different licensing deals in place for VC vs. NES Mini.
The Mini NES should have been designed with an SD style card slot, that you'd load under the flap. Replicating the NES experience.
Then every holiday season you can release new carts of games. And no need for VC support (which adds cost), as they're providing new games periodically through physical media.
Also since the hardware isn't tied to the roms, means that if a license owner decides to screw with you it's easier to just drop their games from the carts.
Also controller cable definitely should have been longer.
SD card slot was never going to happen given how easy it is to use it as an entry point towards accessing the firmware and kernel. And wait, how does VC adds cost, and using physical media doesn't? You'd have licensing and manufacturing to add vs. just licensing for VC support.