Though the leather has a natural abrasive it has very little effect on most knife steels and when it does it makes the edge almost useless for anything but shaving.
With all due respect, have you any credible sources you can cite for this?
I was stropping for about 40 years using my Greatgrandfather's strop before I even knew there was such a thing as compound to use for sharpening. Oddly enough, I was able to get my knives considerably sharper than from just stones, and did not need to go to stones more than a few times a year. I never used my knives for shaving though they were sharp enough to pop hair. Just bushcraft, farm chores, and daily odds and ends. They worked well.
Fortunately I didn't ruin that old strop, but did
waste a whole lot of money in later years on HandAmerican strops that I covered with HA compounds. (This is
NOT to say that HA strops are bad. This
IS to say that putting compound on them is covering up what makes them good!) Had I known the truth way back then I would have only had two good leather strops, (could have been HandAmerican,) neither of them having stropping compound on them, (one free-hanging and one bench mounted) and several MDF boards for compound use. Sparing compound use.
Unless one is machine stropping, or
stropping several knives every day a bar of CrO2 compound the size of a MilkyWay chocolate bar will last just about one and a half lifetimes. Give or take a few years. That's for the recreational sharpener. A professional who sharpens a dozen knives every day, six days a week will obviously use more. Maybe three MilkyWay bars in a lifetime.

If the surface still shows some greenish tinge, the compound is still working. It doesn't have to look like springtime. In fact, too much compound creating too soft a surface limits the polishing action.
Using a compound on quality leather gives you all the benefits of using leather with the cutting action of a better abrasive.
The
ONLY benefit of using leather is the natural silicates found in it. This is why the old "Russian Red" horsehide strops were so good. Horsehide has more natural silicates than cowhide (male or female,) and the "Russian Red" (which, by the way has nothing to due with the country,) is
the name of the result of the method of working the leather called 'boning' which serves to bring more of those silicates to the surface of the hide.
(
Boning is a process by which the leather is worked over the rounded end of a thick pole while being rubbed and pressed vigerously with the smooth end of a large cow leg bone for several hours. It makes a very supple leather whose surface is rich in natural silicates.)
Oil tanned leather and Chrome Tanned (garment) leather leach out most of the silicates from leather. Vegetable tanned leather retains them, which is why all strops are made from vegetable tanned (also called 'tooling ) leather. Putting compound onto the surface of vegetable tanned leather is absolutely no different from putting compound on to the surface of garment leather or MDF board or the smooth side of an old belt. It just costs more to purchase the leather.
While today many retailers do sell sets with leather strops and compound together, it's a good idea to remember that these folks are
retailers... Their goal is to make money. They do that by selling people what people think they want. These sets weren't sold 15 years ago because there was no call for them. But people WERE sharpening knives 15 years ago and wanted perfect edges. The people who REALLY wanted perfect edges were the wood carvers, and they are the ones who began putting CrO2 onto boards to get their knives as sharp as could be. They weren't putting that CrO2 onto leather. That came with the knife sharpening crowd just a few years ago. There are plenty of cites for this in Google. Look up 'Scary Sharp & woodworking.' Right after the 2,000 grit wet/dry sandpaper they would put CrO2 onto a paint stirring stick and strop their carving knives with that.
Stitchawl