I really don't think the thickness of the glassine paper is the issue. I'm convinced it's the glue Dennison used. After all, it's the glue we're always talking about when we say the hinge ripped the paper when we tried to remove it. In the "olden days" when glue was made of animal parts (old horses = glue factory), glue was different than the purely chemical glue manufactured today. Modern attitudes make it far less likely for companies to make animal glue using horses, pigs, or whatever. From an online "Slate" article: "Animal glue, popular for thousands of years, has fallen out of fashion in recent decades. Over the second half of the 20th century, synthetic glues have become more advanced, as they are cheap, uniform in quality, and have longer shelf lives." Apparently, though, some "animal glue" is still made, and it's preferred by bookbinders. So why this glue can't be used for hinges -- assuming that the new hinges use different glue, of course -- I don't really know.
But whatever the reason, new stamp hinges stick much more permanently. That would be considered a very good thing if you made glue. However, in the world of stamps, that's not so good. We like our glue to hold well, but also be easily removable. Like rubber cement -- which I sometimes wonder about as a hinge substitute(?). Or is that nuts? Whatever glue (or paper) Dennison used, it was just right for mounting -- and removing-- stamps. It held well, but it removed smoothly without tearing anything. It's a bit like the glue on "Post-It" notes, but I've been told that apparently that glue is not very permanent which Dennison hinges were if you left them alone.
Why don't we know the composition of the glue Dennison used? It's a mystery. You'd think an average chemist could scrape off the back of a few Dennison hinges and determine exactly what kind of glue they used. They do that sort of thing in police shows all the time!

So the real question, I suppose, is why no one has taken that easily-discoverable composition of Dennison's glue and re-manufactured it? If any collector is also a halfway decent chemist, or if you know one, maybe you'd like to run the test and let us know. Or ask your kid to do this for their next Science Fair. Please.