Good question! It can save a lot of effort, but there are a few problems with it. For one thing, most powered screwdrivers are enormous and overpowered for this kind of application. This isn't to say I haven't taken computers apart and put them together with a milwaukee hammer drill, I have and I'd do it again, but it's very awkward to use something like that on camera and there is a risk of rounding out heads, etc.
There are smaller drivers, but most of them are still pretty damn big, still don't look good on camera, and are still overpowered. Then there's a big leap, and you have the ones that are about the size of a thick sharpie pen. I own one of those and use it often for laptop repair, but the motor is pathetically weak. It's not sufficiently geared down to remove any screw that's more than finger tight, so I just end up bailing out to hand tools anyway.
Then there's bits to consider. I don't think I did it in this video, but in later ones you'll see me using an ifixit kit (shockingly good quality, I was surprised, they look like crap until you handle one) because it happens to contain a very convenient assortment of bits, including several tiny nut drivers. Those bits fit in the sharpie-sized driver but usually it doesn't have the oomph I need, and I can get them in normal 1/8"-shank size, but then if I do need to use a precision driver they won't fit.
And then, finally, there's just the fact that doing things manually lets you get a feel for them. If I start taking something apart and realize that all the screws are only finger-tight, that tells me something; if they're cranked down so hard I hurt my wrist getting them out, that also tells me something. And of course, there's just a material nature to doing it all by hand that has some appeal, and also looks a lot better on camera. :p
Basically, I switch to electric drivers when I have a lot of work to do that's all the same. They're fantastic for bulk dismantling, and I used one back when I was rebuilding used PCs all day long, but for piecemeal work I prefer to do it all by hand.