Using the right compound (for VG-10) on a strop will actually remove the burr quickly and not just straighten it. White rouge or grey AlOx compounds that I prefer to use on a denim strop will get VG-10's burrs gone in a hurry, leaving the edge polished, durable and keen.
Plain stropping with no compound or a poorly-chosen compound (like green) won't do much to remove VG-10's burrs at all. The whole key to removing these burrs is by abrasion at a very light touch, using a compound that easily cuts the steel to remove it, instead of trying to break them off by folding back & forth. Abrasion with a light touch can be done on a stone too; but VG-10 makes that more challenging on a hard stone, creating or exacerbating burrs against the stone, if the touch isn't just perfect. That's why for me, in the specific case of VG-10, the 'cheat' method on the right strop with the right compound makes handling these burrs a breeze by comparison.
A burr -- or wire edge -- is just weakened metal pushed up into the apex during sharpening. The coarser the stone, the harder the pressure, the bigger the burr.
When both bevels meet at the apex, you will get a burr with every stroke of your sharpening stone -- that's not a flip, but a new burr. It leans off to the non-sharpened side. When you switch your stone to that non-sharpened side, you will cut off the old burr, provided you don't change your stone angle. And as you continue the stone stroke, a new burr will form on the other side.
Some burrs can flip with edge-trailing strokes, but typically you're not flipping the burr, but just recreating a new burr on the other side. The "flip" is an illusion in most cases.
As you go through finer grits and put lighter pressure on the stone, the burr gets smaller. When you strop at this point, you are not cutting off the burr, but just straightening it up. The apex will be sharp. It will not reflect light. You will not be able to feel a burr with your thumb, but it will be there as weakened metal in the apexed edge.
However, you will think you've removed the burr, just as you described.
Stropping removes so little metal that it would take longer than you think to whittle the edge down below the damaged metal in the apex.
Stropping will remove a micro-burr -- a really, really tiny burr that is too small to feel. And it will polish (refine) the micro-teeth left from your last stone. It will also align the edge apex if it is not too out of whack.
My question to you is how you know you've removed the burr by stropping? You have no way of seeing how structurally sound the metal at the apex is. And that's the only way to know. My belief is that you have not removed the burr, just straightened it to the point where you can no longer detect it.
The real key to a properly finished apex edge is not just how sharp it is, but how long it lasts -- and a long-lasting edge can be achieved only when your apex is cut from virgin steel.
A lot of people have written that the super-wear steels, like S30V, lose their fine edge very quickly, but the working edge lasts a long time. Larrin has dispelled that myth, but the reason it persists is because people are leaving damaged metal in the apex, especially on these super-wear steels where the burr is more resistant to full removal.
They lose their fine edge quickly because the apex was comprised partly of weakened steel.
