The way we teach mountain pose - and indeed all our poses - is with feet lined up under hips. People often ask why, especially if they've been taught a more traditional, less biomechanically-focused style of yoga and have been taught to have big toes touching.
So, why SHOULD you stand with your feet hip distance apart?
If you can line up your legs to be vertical - in your plumb line, stacking your bones to balance and bear weight you will be using your body in the most efficient way, rather than having any particular group of muscles working too hard. It's much easier to do this with your feet under your hips because of how gravity pulls on your body.
Gravity naturally pulls everything straight down in a vertical line.
When things are in a straight line the weight travels easily down the straight line, as Nadine is modelling quite happily below (her hands are on her hip bones to give you a visual of where they are):
When things aren’t in a straight line, naturally the weight still wants to go vertically down in line with gravity.
So, to get to a point that is not directly below where the weight is, a horizontal load is needed to get the load to where it needs to be. You'll notice Nadine looks a lot less happy modelling this situation. She says in order to not fall over, she had to stick her butt out and pop her ribs forward (not plumb at all). Plus, her knees and ankles were hurting.
We aren’t intended to contract any muscles when we stand.
The muscles simply stabilise us. Ideally, there’s no contraction, no lengthening, no stretching. But when you have your feet wider or narrower than your hip bones, or when you turn your feet in or out, this changes the lengthen of your muscles from origin to insertion point. Then you get weird contraction patterns, knee pain, etc.
When you line up all your bones and muscles optimally, the arches of your feet lift too, so you get better support from your foundations.
It’s the same as setting up foundations when we build a house, or houses on stilts: the stilts are vertical, and are not at an angle. Can you imagine what would happen if that house had skew foundations? Yep, same with legs.
If you want to delve deeply into the physics behind this blog post, here's an excellent resource.