That's not a bad idea, but you gotta remember that not all musicians listen to the same songs. So, I could post a song with a particular progression, but if no one has heard the song before and it can't be heard online, what good has it done?
Also, my goal isn't for you to learn songs. My goal is for you to learn musical patterns that make up songs. How well you know the patterns will greatly affect how well you will pick up on learning songs.
One more thing is not all the patterns are as "cut and dry" as they are posted here on LGM. The overall pattern might be there, but there may be little nuances that make it seem like it's something harder.
It's all a learning process. Any beginner won't really be anywhere near the musician you want to be for at least 10 years so you might as well slow down and learn at your own pace.