Interestingly, patent law agrees with you — mathematical theorems, for example, cannot be patented.
In principle, a patent should cover specific machinery/process/material designed for a task rather than the underlying more ephemeral/indefinite concept powering the invention.
The interesting thing is that, of those, machine and process seem like the least conceited. Composition of matter seems more like sticking a flag in infinite ground. But in practice it’s the former two that power most of what I consider an abuse of the spirit of patent law. But perhaps that’s just my personal bias and the bio or materials people will disagree.
What can we say? Profit motive is a strong incentive and lawyers/judges are clever.
Anyways, with 7B people and counting, a term limited right to one idea in the infinite space of ideas seems less harmful than perpetual rights to a piece of land.