The argument seems to be that 1. a theoretical computer scientist is not a general mathematician and wouldn't be hired to a tenured math position ("sociological argument") and 2. treating it as a branch of math is "harmful" to theoretical computer science.
There are hints about what OP believes TCS is which isn't math, but I wonder why not make that an explicit argument — that would make it much easier to reason about and argue either for or against.
Without that, neither 1 nor 2 make a convincing case for anything: 1. a Linear Algebra expert might not get a position in a Statistics department either, and 2. it'd be useful to show some "harm" before you claim anything being "harmful". CS is also lucrative enough that it pays to have a dedicated faculty just for CS too (as in, it attracts students, contracts with external parties for a university, etc).