there's a good case for a single speed setup if one's bulk of the mileage is on flat(ish) terrain - better efficiency, reliability, easier cleaning, lighter, cheaper to run. big part of commuters i see in london don't bother changing gears anyway.
I often do hilly rides in the Chevreuse Valley area, but if I ever have two bicycles, one will be a single-speed. In riding with others on single-speeds (actually, most of them are fixed-gear machines), I have noticed that most of them are noisy … intolerably noisy. I wonder what they’re doing to these poor things to get them to sound like that. Still, their riders sound happy!
A SS setup is usually very quiet when the parts are new; however once the chain is a little worn there is a conflict between elimination of slack and the need to let the chain 'ride out' on the chainwheel teeth, I.e. to the diameter at which the (longer) chain pitch matches the pitch of the teeth.
If the slack is removed from a slightly worn chain (leaving (say) a nominal 1/2" free play) then the transmission can become very noisy. It is also likely to be wearing very quickly too, since the loads cannot be shared between teeth in the normal way. Any time such a transmission is noisy, it is very likely that the chain rollers are moving around on the teeth whilst under load, which causes everything to wear more quickly than normal.
The only situation where I will tolerate noise for any length of time is when I have let a chainring become slightly hooked, and it is being forced to mate with a new chain. It rarely takes more than a few hundred miles to go quiet.
IME if everything is allowed to wear together, and enough slack is allowed/tolerated (i.e. without unshipping) a SS/IGH transmission remains quiet and smooth even when the chain is worn to ~1.5%. It ain't a smart idea to run chains out this far if you don't have a steel chainring though; the chainring gets into a pretty bad state otherwise. Presumably there is some loss of efficiency through running with a worn chain but this (unlike noise) usually isn't noticeable. When everything is knackered, a new chain and sprocket (less than ten quid for an IGH....) and you are good for another few thousand miles.
However do note that on a fixed gear setup any chain slack is not usually tolerated; for one thing the chain is very likely (more likely than with a freewheel) to unship and for another the sensation of a slack chain with a fixed gear is pretty nasty. Some riders like the feeling of a slack chain less than the noise, so they choose to have noise. Note that running a really quiet fixed gear setup is not a cheap business; good fixed sprockets are quite expensive and even if they are evenly worn (i.e not hooked, run smoothly under load still) any wear on the sprocket also generates a small amount of backlash, because the chain rollers are no longer located positively between the teeth. SS freewheel and IGH setups are a lot more tolerant of chain/sprocket condition.
BTW thanks for putting the arrows and labels on your photo; it is exactly as you indicate. FWIW I can usually spot hooks that are bad enough to cause skipping but ramps are more subtle. It is clear that the difference between a tooth shape that will cause skipping and one that won't can be as little as about 10 microns of metal in the wrong place.
One of my mad ideas is that if you have a couple of ramped sprockets that won't play ball with a new chain, it might be that they can be 'shown who is boss' by being used in a (tensioner-less) SS setup for fifty (slightly noisy) miles or so. You could keep a new chain for this exact purpose, perhaps.
Having run a few different systems over the years (maillard freewheels, sun tour freewheels, shimano UG, shimano HG, etc) the same thing happens with all of them; you run out of the sprockets that you use most/wear fastest before any of the others.
Some sprockets
a) are favoured and see more use than the others and/or
b) are small-ish so wear more quickly anyway and/or
c) appear in every freewheel/cassette you might build (eg if you use the same system for racing and touring)
so with my sun tour 'New Winner' freewheels (BITD I was a sucker for more cogs; I was running 7s in ~1979, i.e. five years before it was available in Dura-Ace) I basically ran out of 15T and 17T sprockets first. They say the only certainty is change; for a few years there were three bike shops I could go to which each had a fully loaded Sun Tour sprocket board and I could keep things sweet and have the exact ratios I wanted by just buying a few extra sprockets.
With a shimano 8s cassette system you could perhaps use odd UG sprockets in the most-used positions. These sprockets are reversible so you can get extra life out of them. Gawd knows where you would get them now though. Other options include shimano DX BMX sprockets eg
https://www.bike24.com/p217742.html and Brompton 6s sprockets/SA S3X sprockets (both found on this page)
https://www.sjscycles.co.uk/sprockets-hub-gear/?page=2both of which use a modified freehub spline design and are available in 3/32" format. Again some of these (with a small spline modification) are reversible.
If you start using odd sprockets in an HG cassette then shifting performance is likely to be degraded; you may or may not tolerate this.
cheers