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I don't feel qualified to answer your first question, as I'm just very inexperienced with serialism. I'm going to spend my time answering your second question.

> Isn't a point of music theory to probe the structure behind compositions, even if they're not mathematical?

Yes, but in a more specific way than you are thinking. Theory follows art. Every time.

To understand this, you have to understand the difference between the goals of the composer and the goals of the theorist.

The goal of the composer is to write music that brings them satisfaction of some kind. This might be an emotional response, this might be monetary benefit, or it be for philosophical reasons. The core thing to understand is that a composer is focused on expressing something, whether it be programmatic or abstract, personal or impersonal. There is a vision behind it. The composer is then focused on using the tools they have available to them to accomplish that vision. Those tools do not  have to fleshed out. They can have holes. They are there to be used, not looked at. Imagine theory for a composer is like a hammer. It doesn't matter if the hammer is full of dents or is covered in paint. If it can still drive a nail, it has achieved it's purpose.

For theorists on the other hand, the goal is to explain the music to the largest degree possible. They are trying to understand the ways that the music affects people. To do this, they have to dive even deeper than a composer does. A composer can be satisfied knowing that a specific sound will typically produce a certain emotional reaction. The theorist needs to dive deeper and understand why that sound creates that emotional reaction. They need to look even further into the construction of the music.

The result is that the theory a composer used to write the music is very rarely the same theory that this music is eventually explained with. This is seen with classical era composers. They would have written and analyzed music using figured bass. We now use roman numerals to accomplish that same task. As theorists began to understand the construction and logic of the music on a deeper level, they created a model to show those connections.

Another example is modern chord loops. These don't match functional harmony too strongly even though that is often the model used to explain it. The theory for chord loops has only recently started to develop, and it's still not a particularly popular way of looking at the music even if it may explain it better.

This is why it's worth trying to come up with separate theoretical models for understanding this music. While the composer used certain theoretical models to help them get music on paper, theorists need to look even deeper if they want to explain the why and the how of the music.