Elines ... To a degree you're right. I use thin, firm leather on the strops I make for sale, and use myself, for this very reason. Applying pressure to to thicker or softer leather with the knife edge will deform the leather beneath the edge to the extent that it can actually round off the edge as you work (where the leather is springing back up immediately behind the edge as it passes)
Applying pressure as you strop however, is the most effective way I have found of doing the job of fully polishing (and therefore sharpening) an edge as it makes the compound (paste/Starkie Blue/Flexcut Gold .. whatever) cut more efficiently.
You can spend half an hour or more lightly wiping the edge along a softer, or thicker strop, or you can spend 5 minutes doing it with a bit of elbow grease on a strop with thinner, firmer leather .... Your choice

You have to remember that you are only really using the leather as a holding medium (like a wick) to hold the compound in place so you can effectively use it to polish the edge of your blade. It is the compound that cuts the steel, polishing it. Once the compound is blackened with removed steel and begins to glaze over, you are best to scrape this 'used' compound off the strop and re-apply fresh compound. This will keep the system working at peak efficiency, saving you both time and effort and giving the best results.
It's very similar to using fresh wet-n-dry instead of a old worn, and clogged, piece. Better, cleaner, faster, and more efficient cutting is done with fresh abrasives, every time
It is for the very same reasons that I don't like to advocate the use of a mouse mat and wet-n-dry for sharpening convexes (or any other type of edge for that matter). The mouse mat is inevitably going to be softer than almost any leather you're likely to use, and stands a very good chance of rounding off the edge of a knife rather than sharpening it. A firmly backed abrasive medium gives you far more control over the angle at which you are finishing the edge.