Actually Gershwin -- along with Cole Porter, Irving Berlin, etc -- WERE popular music, and I think they'll easily stand the test of time.
I mean, one issue you haven't addressed is that music from before the 20th century was difficult to preserve. There were no recordings. It was hard for composers to get noticed outside of cultural events and royal functions (depending on the location). Music was written down, but paper corrodes. It was difficult for people to spread the word about musicians. The composers you note have survived largely due to groups of people who were staunchly committed to preserving their works. If a composer wasn't lucky enough to get one, that was it.
Now, we have recordings, and excellent methods of preservation, not to mention communication. Someone in China can record, upload, and send me a concert they heard minutes ago. And though hard drives die and computers are hardly immortal, I think all these changes will allow even marginal bands to stand the test of time. I mean, thanks to the internet bands from the 20's and on who practically no one had ever heard of are now being rediscovered and developing cult followings. How cool is that? I think if anything, we're going to expose ourselves to even more old music as time goes on -- not less.