Music Learning

I used to try to learn songs on the piano by going right to playing the songs, taking little to no time to get the chord names into my brain outside of what was necessary to play the songs. The result was that I could play songs that sounded quite nice. The drawback was that if I didn't play the songs regularly, I forgot them.

I'm wondering about that as I think of learning chord melody on the guitar. I bet I could memorize some nice stuff, but am I really learning anything other than how to play a particular song? 

I suppose if I learn to play a ton of songs, eventually it will get easier and faster to play other songs. But the problem is that my brain simply cannot keep in my muscle memory more than about two songs at any given time. So I learn two, and I have to keep on repeating them to keep them in my memory, and as I try to learn another song, and another, things get very time consuming (keeping the older songs in memory while adding new songs).

So I brought this up to my online jazz teacher who got back to me that he'll respond with his answer soon when he has a live Q & A. 

I'm wondering if the answer is to learn chords (on piano or guitar) in isolation as well as in the context of learning songs?