Sure, but they would make more money with more production.
Think about it this way - if you knew something was always going to be available, any time of the day... it kind of diminishes your urgency to buy it, right?
I think it's an outdated policy, like waaay outdated and mostly in response to the overproduction of the early 1980's that hasn't been a threat in decades. But I can see the merit of acting in this counter-intuitive way for building brand value, on occasion. But at this point Nintendo has a pretty high established brand value (especially in comparison with how small the company really is) and they don't have to keep pulling stunts like this.
You could compare it to Amiibo the difference is they brought back the Amiibos that were vastly under-produced and that helped those get them later. Meanwhile with the NES mini they are just like hmm, lets announce this final shipment letting all the scalpers know that we will never make another one.
If anything the best way to do this type of strategy is VASTLY under-ship the first 1-2 shipments then 2-3 months later ship the fuck out of it. That way everyone overreacts to how hard it is to get in the first 1 or 2 shipments and then when the 3rd comes on like a tidal wave everyone buys it since they missed out before. Sony somewhat did this with the PS2 where the console was hard as hell to find for the first 4-6 months of its life cycle but then 1 year later or so they were readily available.
They sometimes do that. Sometimes they don't. They don't really carry a specific strategy with it. The only reliable thing they will do is really short supply upon first release.
The only Nintendo product I can think of in the last 5-10 years that they really over-produced it was Metroid Other M. They miscalculated so badly on that that they ended up selling copies for a dollar.