I think what you're missing is that Apple pursues high-margin endeavors, and competing with a $300 NUC isn't going to be a high-margin business. Some easy money for Apple would be to sell OS licenses for Intel NUCs.
Apple could sell a $300 NUC for $600 and people would still buy it. The issue is that Apple doesn't sell anything decent in this form factor that runs macOS.
I agree that they could and should - I'm just speculating as to why they don't. As they probably could make their desired margins, it must be they would consider it a "distraction" from future endeavors (VR, cars, etc.)
The NUC in question, the NUC7i5BNK, is $620. That is without RAM or storage, so add another $50 for 8GB RAM, $80 for a 128GB M.2 SSD, and $100 for a Windows license. Total price is $850. This guy isn't cheaping out, he just wants more hardware for his money.
$700 at Apple gets you a much slower 3 generation old i5 with a 1TB hard drive. But, with MacOS.
It's one thing for Apple to charge a premium for better hardware. But that is NOT what they're doing. They're charging the same amount for ancient, inferior hardware.
Never pay MSRP, the NUC7i7BNK is going for $500 ish on preorder. The NUC7i5BNK is going for $400. The i3 version for $300, and the celeron or whatever is below the i3 is going for $200 ish.
However the nuc generation7 i5 is the lowest model with the iris graphics.
There are some little things a Mac Mini has that you can't get by just (essentially) Hackintoshing a NUC.
For example, Apple's custom UEFI, plus a Bluetooth controller that boots in HID mode and loads configured pairings from NVRAM, allows you to "hold down [key combination] at boot" on your Mac Mini's Bluetooth keyboard.
Or the fact that all the desktop Mac models have internal speakers (and not just the motherboard PC speaker kind) and internal microphones, so OSX can guarantee it always has those devices available to use to play system event notification sounds, or for Siri, or for FaceTime, or for visual-impairment accessibility tooling, etc.
Or the fact that you can still plug FireWire or DisplayPort devices into a Mac Mini through its Thunderbolt port (with a passive adapter to map the pins) and the motherboard will happily accept the device; whereas no PC would have any idea what to do with those wire protocols, even if you plugged them into the port of an explicit Thunderbolt PCIe card you bought.
If you could get these things from a NUC, then sure, there'd be no point in the Mac Mini.