Most lenses are sharpest around the middle of their aperture range. So f/5.6-8 is the sweet spot for the best recording. The middle happens also happens to be the boring range of the lens - depth of field isn't extreme, nor really shallow to allow isolating a subject.
The only time I shoot f/16 or f/22 is when I need to really slow the shutter down (moving water and didn't bring ND filter), because if it is extreme depth of field you are after in a landscape, this can easily be achieved with
focus stacking several clean f/8 exposures, without getting
diffraction issues from the closed aperture, or risking motion blur should you not use a tripod (weight...). Focus stacking also lets you create images with extreme depth of field technically not attainable with the lens itself, even at f/22. I've even used this with a 14mm ultra wide at times, when I needed 12 inches to infinity in focus.
Bringing a good ND filter will get you blur when you want it without having to use f16/22 - a must bring in snow conditions, although a polarizer is usually enough with snow. For the ghostly moving water effects you really need a good ND filter - neutral extra dark sunglasses for your camera. I forgot to pack my ND100 filter this summer
You can always improvise a tripod, but you can't improvise the ND filter.
Wide open is the problematic thing to justify for me: to get good results (clean background blur) you need a really fast lens. Fast lenses are generally heavy due to the large chunks of glass required to capture all that light. Fast glass only has one additional benefit in the backcountry, and those star photos Chris took are evidence that he took full advantage of that capability. I've been too lazy to carry very fast glass on long trips, and my night shots are pretty crappy as a result of that. Fast wide angle glass starts at f2.8 (zooms and ultrawides), and goes up from there. You rarely shoot these wide open, but to get all the light you can get you need a lens to be even faster than f/2.8 to be able to get sharp results at that setting. Wide open is usually soft, especially in the corners. A lens rated at f/1.4, though, will be significantly sharper at f/2.8 than a lens rated f/2.8 to begin with. I have a 55mm f/1.2 which is superbly sharp at f/2.8, however, it is a pretty useless focal range for sky photos at night, and it is very heavy, so I never took it on a hike yet.
I am saving for a Rokinon/Samyang 24/f1.4, the ideal night sky lens for those who can't afford the big brand name offerings ($2k), but it weighs 750 grams and I have my doubts about carrying that down the trail. This summer I left my 500 gram 14mm f/2.8 in the truck when I lifted my pack before the first day of the hike - that's usually where all my great intentions to carry extra camera gear come to an end
You can rent just about any great and expensive lens, so if your trips are short term that's a way to get your hands on the tools. If you do 100+ days at a time in the mountains, well, renting ain't the most economical way...