I think the word "equivalence" should be banned as it's an instant flame bait.
My 2 cents though: shallow DOF is the bane of my existence. Well, maybe not so tragic, but I don't like being forced to stop down a lot just to get a meaningful part of the subject (or a group thereof) in focus. That something isn't blurred into an unrecognizable mess doesn't mean it's rendered in a useful way; half-soft image (or parts thereof) is still that - soft and therefore not beneficial to displaying the subject (if it falls into such an area). Therefore shallow DOF shouldn't be peddled as an universally desirable effect.
Not that there's that much difference (that you would be able to see in a blind test) one stop apart, or between APS-C and FF crops shot at the same aperture (and so being one stop apart, by this logic). Therefore: peace.
P.S. I may be a little thick but does anybody really calculate the scene in that way - starting with "I need a precise focal length X and aperture Y, if I can't get that it all goes to hell"? I start out by looking into the viewfinder and deciding if I like what I see, if it's too narrow I don a wideangle, if it's too wide I don a telephoto. If I don't get enough DOF I try to stop down (but more often than not I just shoot, I don't usually get gross errors). That my 16mm f/4 lens becomes (or doesn't become) a "21mm f/5.2" or whatever else means zilch to me - I don't think in these terms, I just shoot.
You mean to say that shallow DOF is not for you. That is fine.
Weird thing: people take equivalence explanations as "this camera is better than that camera". But it never is about that.
Also a weird thing: not understanding that equivalence is handy when you go from one format to another format. So, you shoot APS-H. For you, a certain lens means "wide angle" and a certain lens means "portrait". You know that 16mm means "pretty wide angle", so you put that lens on your camera when you want to use a pretty wide angle.
Now suppose your girlfriend one day decides to give you a present, a Olympus OM-D EM-5, because in her idea you should have a small camera for when you can't take along your big DSLR. And you do not want to seem ungrateful and really want to use it. But you want a pretty wide angle lens to go with it. What do you do? You get an EQUIVALENT focal length lens. So you have to calculate in order to get an equivalent lens And it turns out that on that Olympus a 10mm lens is equivalent to that 16mm on your APS-H camera. So you know what to get.
That is handy to know, right?
And then the DOF question. Not for every photographer shallow DOF is something to use. We get that, everybody thinks on a different level, has a different style, has different subjects and different sensibilities and sensitivities. Understanding equivalence goes both ways. If you know from experience that f5.6 gives you the DOF you want for street photos with say your 24mm lens on your APS-H body, it is easy to know that if you want to use that gifted OM-D EM-5 in the same situations that an equivalent aperture is f3.5 or f4.
A bit silly to say that the difference between APS-C and FF DOF wise is only 1 stop. It is more than 1 stop, more like 1 1/3rd stop. And if 1 stop is so silly, why do people buy f2.8 lenses instead of the cheaper and lighter f4 lenses. Why are f1.4 primes being bought over f2 or even f1.8 primes. Why is there a market for the f1.2 primes when there are f1,8 primes.
Answer: 1 stop difference in DOF is a big step.
Don't make everything about "me" (meaning you, not me) in discussions, it is fine when something is not for you, and it is fine when it is for someone else. I get that, I get that that some people like EVFs, and I get that I like OVFs. In discussions, I then point out that for ME OVF is preferred, but that for others that may be different.
For ME, shallow DOF is a tool I often use for my photography. I am not alone in that. So for me, shallow DOF is something to take into account, while for other photographers (you for instance) it is not. That is fine. Does that mean that it should not be discussed and explained? Of course not.
Shallow DOF in my photography:
It is an important stylistic tool, that I use and need to understand both on full frame 135 format and APS-C. Understanding that the crop factor both influences the FOV and the DOF with is something every photographer should understand. So they can get the image they envision even when they use cameras with different format sensors.