It does because calling that function adds a new control flow edge out of the block it is in, which means you can no longer prove certain cleanup code can safely be elided.
Additionally the fact that C++ does not annotate whether a function throws in its signature that means you need to generate unwind data for most non-leaf functions since (short of whole program LTO) there is no way to safely to know that the functions they call don't throw. That means the size of the metadata necessary to support unwinding grows with the size of your binary, not the portion of the code using exceptions.
Finally, C++ exceptions are dynamic, which imposes a higher cost when they are actually used than a static exception model.
In general I suspect that explicit error handling (as is done in the Swift ABI) would result in better code because it would make the control flow edges more optimizable and optimizer could safely assume many functions don't ever need to be unwound. It would certainly make the binaries smaller due to the reduction in size of unwind tables (although some people including Stroustrop[1] argue there are ways to do similar optimizations to elide unwind data with existing C++ compilers, but I am not sure if anyone has ever built such an optimizer).
There is some discussion about adding a static exception model (with annotated functions) described in P0709[2]. Various parts of that are controversial, though I hope the committee eventually finds a way to agree to some variant of it, because it would allow unification with other languages (it is semantically equivalent to Swift Error handling), and there are even C proposals that would be interoperable[3].
Full disclosure, I work on a dynamic linker written in C++, so I spend all day long writing C++ code that is built without exceptions or most of the standard library, but is part of the runtime machine that enables exception handling.
[1]: http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2019/p194...
[2]: http://open-std.org/JTC1/SC22/WG21/docs/papers/2019/p0709r4....
[3]: http://www.open-std.org/jtc1/sc22/wg14/www/docs/n2429.pdf