Many videos and tutorials from the much respected internet woodworkers show them always going from a coarse medium through to a fine.
I think there are three key things here.
With respect to a few of them, the category "Internet woodworker" does not in general mean you're getting info from the best and most experienced craftsmen. Always worth bearing that in mind to begin with.
The second is that every workman's tool wear, and acceptance of same, is slightly different. Using equivalent tools, if one person is working much more on hardwoods, particularly harder or more abrasive species, and another is almost entirely using common softwoods their respective need to sharpen will be wildly different.
The third thing is, and this is the most important probably, there is a massive gulf in the sharpening routines from one end of the spectrum using one stone, sometimes with no strop (yes really) to the guys at the opposite end with five or more stones routinely used for normal sharpening (honing). Additionally some sharpen a bit and test their edges to see if they've done enough, others work through a sharpening routine by rote and therefore don't have to check because they know that it'll always have returned an edge to working sharpness (this is Paul Sellers for example, he's one who specifically advises always working through from coarse to fine surfaces and ending with a good stropping).
Now on to what you do specifically.
20-30 strokes or so on a 3000 grit water stone (this is enough to get a burr the full width of the blade), 20-30 strokes on a leather strop with some chromium oxide compound, and carry on.
It's working for you and that's the main thing, but, for some the fact that 20-30 strokes are needed indicates that the stone you're using is a little too fine1. There isn't a single standard here by any means but very broadly speaking you should be able to turn a burr in 10-20 strokes and doing it in under ten can be a realistic goal.
What is the benefit to working through the grits for a common touch up?
For most people, there isn't one. Doing so is simply wearing away more steel than is necessary to get back to sharp.
Now in the grand scheme of things this excess wear is NOT a big deal. The entire lifespan of an edged tool is more than one generation in almost all cases so even if you significantly shorten something's lifespan you're unlikely to notice it :-)
But I don't think anyone needs to go through a full grit progression2 just to deal with common edge wear. You should only need to do this from normal use if a ridiculous amount of time has passed since the last sharpening and any such edge is long past functioning like it is supposed to.
One person's bottom line
If routine sharpening (honing) is taking longer than a couple of minutes per edge you're not doing it efficiently. The fastest workers, honing little and often as almost all of us should, can get an edge back to workably sharp in 30-60 seconds and IMO that's the thing to aim for.
Note: if you can't do it that fast and you want to, then shorten the interval between honings, change your sharpening materials, or both.
1You're honing on a stone finer than the majority of workmen had in the shop for most the last few centuries of European and American woodworking to put it into perspective.
2Especially if it starts at a truly coarse grit and then goes through five or more grits, ending up at a very very fine grit.