Oh.  I thought it went back up after the holidays. My bad.

it went back up for like 10 days, then MS dropped the price back to 349$

Well then, that's neat. Nothing really to see here (goes back to waiting for Halo 5 custom Xbox 1 announcement)

Calling it a price cut is technically incorrect, indeed. Anyway, despite being a different thing, it is intended to get the same effect, as it lowers the entry price, and it can be put in a more positive light for the brand image than an early price cut. It was a good move IMVHO, I'm not a MS fan, but I'd be obtuse if I didn't admit that sales clearly show that MS fixed initial mistakes with XBOne far better than Ninty did with Wii U. Removing kinect has its drawbacks too, without incentives 3rd parties won't implement it in games except for optional features, but mostly they weren't adopting it anyway with true kinect games requiring it mandatorily, and probably many lazy attempts would hurt kinect more than benefit it, better getting fewer ones, even partially funded by MS itself, but properly designed to use it in an enjoyable way.