There is very little incentive to choose XBO over the PS4 for the average consumer at this stage even beyond price. I'm really not convinced keeping every XBO SKU $50 below every comparable PS4 SKU will make any difference at all without software support in the form of exclusive games and extra content.
If MS chooses to cut any sort of profits or even take a loss on each initial unit sold, they'll end up selling many of those units to existing PS4 owners looking to pick up a secondary console on the cheap or dedicated XBO owners who want another XBO which is not what MS wants. They know they have to sell to the previous generation hold outs if they want any sort of decent attach rate for software sales.
One could argue that's exactly what MS has been trying to do with XB360 BC, but that doesn't seem to be creating any sort of pay off based upon XBO hardware sales; it's just a nice bonus for existing XBO owners who already replaced their XB360s.
In the end, keeping that $50 price advantage would mainly result in a $50 loss per unit rather than convert into significantly greater sales to new (non 8th gen) consumers which bring higher software attach rates.
MS should probably concentrate on releasing their hardware update which should be smaller, use less power, come in compact, lighter packaging and a significantly lower BoM before doing any more price cutting.