Wow, what a scary notion. Imagine that, no more room for originality in music.
But hold on, before we go down this rabbit hole, I want you to watch this awesome video blog by the guys a V Sauce called "Will We Ever Run Out of New Music?"
The thing is, not only have us humans settled on certain lyric and melody norms, or "commons", since the 60's we have also been smitten with common arrangement standard too! This largely consists of verse, chorus, verse, chorus, middle 8 (or bridge) and outro chorus.
Furthermore, songs tend to cluster around the 3:30 length and as shown in the video, we make do with very few chords.
Now I know this doesn't apply to all songs but as a general rule, we do see a very narrow field pattern when in comes to popular music structures.
To further increase the likelihood that we'll reach stagnation, I'd argue that the human ear needs about 2 seconds to process a “chunk” of music for any real meaning. In 2 seconds I can hear the beat, speed, melody etc of a piece of music and compare it to all the songs stored in my memory banks to find a possible match.
So, rather than talk about the squillions of possible combinations available to the human ear, we're probably looking at magnitudes less when applied to popular music.
There could be a strong case to say that out of the estimated 200,000,000 songs out there, an unsettling percentage of them are “almost” carbon copies of large sections of other songs.
But let me steer you gracefully back to a reassuring thought. What we are doing here is arguing the point that a group of chords, mixed with a tempo, time signature and vocal tune are likely to repeat given our natural bias towards certain “common” structures.
But, when we mix in sounds, production values, unique vocal tones and live musicianship, the variations on expression must be astronomical.
We may always face the issue of hearing familiar songs, but one human brain couldn't hold enough clear memories for this to become a serious problem I don't think.
The wonder of individual expression is such that even two songs using identical chords and melodies will arouse hugely unique emotions in the listener. Subtle variations in the lyrics, vocal tone and emotion, how something is recorded and the "mood" of the overall harmonics is enough to distinguish any two songs.