I actually don't think that learning specific songs individually makes a person a better player per se. (It does make you better at playing that particular song though).
I think that learning chord progressions and rhythm patterns gets you into the zone faster.
Just about every song on the planet (including rock, blues, classical music and jazz) is a derivative of one that has gone before.
There are thousands and thousands of songs that use the same basic progressions.....but are disguised to make them sound different. (a slight tweak here and there).
And song-makers have been doing it since day one.
For instance......if you know how to play minor blues in any format ( 8,12,16, or 32 bar, let's say) you have just opened the door to a massive amount of songs (not just one song).
Many of the Beatles songs (and other famous bands), for example, are completely formulaic....and if you know the progressions they are using you can immediately play a lot of Beatles songs ...not just one.
Yes.....many songs have some of variations...that's the trick:- to put a spin on it so it sounds unique and different.......
But no matter what type of music it is.........the chord progressions used in that genre or style are basically very repetitive in nature and are used over and over and over again.