I can't speak for "most experienced sharpeners," but I speak for myself, of whom has been sharpening knives for over two decades. I am not a guru, I am not a professional knife sharpener, I'm just one of those seemingly rare Chefs of whom sharpen their own knives, and I get my knives sharp... scary sharp. When I was young I worked as a mate in South Florida on offshore fishing charters, and learned how to sharpen my filet knives so as to do my job. I have been a professional Chef for almost 23 years, and I have to sharpen my knives to execute my job. Not for money, not for show... for work - to make the tools work.
When sharpening, I use edge leading & trailing strokes until I've ground down to just before where I'm happy on my bevel. Then I transition to solely edge trailing stokes... basically stropping on the stone. Once I've finished my edge leading & trailing sequences on each stone, I finish with a trailing only sequence before progressing to the next. Then on to the next stone unless the prior stone was a low grit stone in which had generated a burr. Then of course, I take of the burr before progressing.
I have used, with success, my Kityama (8k or 12k depending on who you talk to) simply as a strop to touch up my knives.
I had stropped after sharpening with newspaper draped on my last stone of the progression for about 2 years. That was when I really started researching sharpening; rather then just doing what I knew, which did work very well. The newspaper method was gleaned from Master Bladesmith, Murray Carter, and it worked. Or so I thought, until I used a real [leather] strop.
This forum has talked me into expanding my sharpening kit into a strop, and all I can say is that it is the largest jump in edge performance & longevity, more so, that I have seen in long time. I mean I knew what I knew, and it worked really well so I never looked for more. Now, with a strop, it cuts my time between sharpening noticeably, and touch ups feel like a fresh sharpening. I always made my knives scary sharp with just stones, but I think about how much metal I've ground off for nothing and it bothers me, retrospectively. We live, we learn...