Another factor is that Church-Turing "at first order" isn't a mathematical theorem - (notice "thesis", not theorem).
The thesis is that all determinant computation is equivalent to Turing machines and lambda calculus (which are each computable with each other). This is a hypothesis about the physical world (or the "imaginable" world).
Thus Church-Turing is very significant - but not necessarily mathematically significant, as a mathematical theory, it's taken as the equivalence of Turing machines and Church's recursive functions (but that's just a theorem which only suggests the (nonmathematical) thesis.
The thing is, a lot of mathematicians are much more enamored of the mathematical world than the physical world. For an enthusiastic mathematician playing with high order recursive functions, a generalization of the Church-Turing theorem seems much cooler than the statement about the physical world that the Church-Turing thesis implies.