I've seen both videos. Neither one actually tests the tires in real conditions.
Tire width affects the feel and performance for daily driving, snow, sand, mud, rocks, and... Everything. And I'm not just talking about the carcass width - tread width has an even larger impact.
Load rating also plays into this significantly on light trucks like Toyotas since most skinny tires are dually truck tires, and are therefore E-Rated (which are too stiff to perform as designed on a 5000lb midsize truck).
On Toyotas, I've driven tires from 235mm wide with a 7.5" tread width, up to 13.5" wide with a solid 13.5" tread width. "Skinny" tires (235-255mm carcass width) have some marginal benefits in certain conditions but at the expense of road feel, road handling & performance, comfort, mud performance, deep snow performance, and more. I'll never go back to skinny tires.
I've always been a big proponent of skinny for a given height. But not necessarily just full skinny over everything else. Too far of an extreme will definitely impact on road feel and handling.
285/70/r17 is as wide as I'd go for a ~"33" and they are a really nice mix for most situations. But I've found that rough width is better suited for a 34-35" tire. Way back in the past I've used 235/80r16, 255/85R16 or 255/80R17... all with good results. These are on the skinnier size range, but the 33" size does work well in the 255 width for 16" and 17" wheels.
35x11r17 AT4W, load C, have been my fav all around tire. But the various 285/75R17 are great too. I even tried the very skinny (for 35" size) 255/85R17 mickey Thomson Baja Boss AT. Those were amazing off-road and in the snow. But a bit suboptimal on the road. (they also wore funny and got loud, which soured me a bit).
If on 18" wheels, the 275/70R18 is a great option and taller than the common 285/70R17. Moving up a notch, the 285/70 and 285/75R18s are both a great balance for the 18" wheel if you're looking for a 34 or 35.
I have never enjoyed the ubiquitous 315 width (or 12.5") "35" options, despite trying lots. Never enjoyed the road feel, rain performance wasn't great, and they just looked too wide (to me) for the height. Reminded me too much of the old "true" 33x12.5R15 look.
Moving up from there, 37" tires have always worked best (for me) at a 12.5" size.They also looked proportional. But I'd definitely give an 11.5" a try if one existed. I've only used this size class of tire (or larger) in wheel sizes up to a 17".
Last thought centers around various Toyota powertrains I've experienced really seeming to prefer a skinnier tire, despite what the torque/HP numbers might suggest. (Various Tacomas, including the hybrid 4th gen, LC250, and even 70 series I've driven outside of the country... especially if those had the 1HZ tractor motor).