Yes but with language new words and linguistic forms can be created to provide new material for poetry. Can you say the same for music? How can notes combine to create new material for music once every possible permutation of notes has already been played?
You are making a mistake here in assuming that notes are the "words" of music...they are not. Notes are more akin to letters, but they have the additional modifier of rhythms within them as well.
Words in Western Tonal music are akin to motives. The reason why we aren't recreating pieces from the past is because the language itself (the way motives are used, the way consonance and dissonance is treated, harmonic structure or lack thereof, and the basic compositional methodologies) changes quite regularly.
Composers are constantly experimenting with new shapes and sounds as well.
I'm talking about the mathematical fact that there is a finite number of combinations of notes.
You're neglecting rhythm, tempo, and form, all of which have infinite possible varieties...also, there is only a finite combination of notes when the piece has a specific length, and the notes have a rhythmic limit (no such thing as a rhythmic limit, there are pieces with 2048th notes in them).
Not even bothering to get into the fact that detuning is quite common, or having clarinets and violins playing quarter tones and the like.
Multiphonics, extended orchestral techniques, and most importantly SILENCE suggest that there are an infinite variety of sounds that are used in western music...we are not in any way limited to the pitches of the 12-tone equal temperament scale. Then there's the whole instrumental timbral shifting issue to deal with as well.
As far as other scales and tuning systems go, we use them all the time.
Well, most modern music sounds pretty arbitrary to me
If you're talking about modern orchestral works than it's likely because your ear is uneducated to its types of nuance and concept. If you're talking about pop music, well you're about dead on there for the most part, but once again, just because nearly every song uses some I-IV-V-I harmonic structure does it make it the same song? no, absolutely not.
To be clear, what you've essentially said is something akin to 'Because we can accurately produce all of the discernible colors in our visual spectrum painters will run out of new things to paint.'
There's a LOT more to it than that.