Interesting videos.
The 1st one... well that's not really what I'd call powder - it's ankle deep stuff, mostly on a pisted base. So you're riding that base not the powder. Those riders are also windmilling their arms and generally look very much out of balance... which is precisely what happens. It's certainly possible, but it restricts the fun you can have, because you have to focus on your balance all the time. And it looks awful.
The second video... well the powder's no where near breaking over his head, but perhaps I'm spoilt. Obviously Mr Pochon can ride, and with a style I approve of
That's an Extreme Carving board so it's wider than race boards, which will help.
The third video (instructor with poles). To me he looks a mess on the board, he's almost cranking it at the start of the turns, fighting for balance on what looks like straight forward terrain. Lots of arm action again... he just doesn't look balanced on it.
I ride hard boots in deep powder, and a lot of people are surprised when they realize it's smooth and efficient. I think the reason they expect it not to be is because most hardbooters they have seen in powder were
riding the wrong boards. Just like "park" boards are garbage for riding piste, my race boards are I'm afraid terrible in powder. You need the right tool for the job.
I've ridden over-the-head back-country bottomless with a race boards and it's the most exhausting thing I've ever done. You have to fight for balance even on the simplest runs. Bigger boards (eg GS) are easier, but it's like riding a plank: the flex pattern (particularly the tail) is not designed for powder. No one in those vids was riding trees, but if they were then the tail issue would cause them extra difficulties.
My 2p... yes, you can do it, but it's like trying to peel an apple with a butter knife: why would you want to?
Real powder boards are designed for powder.
So on the OP... well, if you don't get a carve board which is too race-specific, and if you mostly ride resort powder, then you may find it ok if challenging to ride that board in powder. If you find it hard, then just rent any old powder board and you'll find it very easy. Eventually you may end up like me, carrying two boards with you when you travel: one for powder, the other for resorts.
). I like high speed riding and am thinking of buying a new board that would maximize my speed and performance.
"Powder carving": 
Not really fast but enough for relax and get fun 
