The OP mentioned nothing about organizational costs, I was talking purely about performance. The OP was incorrectly claiming you'd spend more time in C++ allocating memory, not less.
Your argument is puzzling. Reference counting is a particularly slow kind of GC. It makes you spend more time freeing memory, not less. And it does nothing to reduce the cost of allocations either. On the contrary, a generational GC can allocate short-lives objects virtually for free—much better than the system allocator. The advantage C++ does have is the ability to control memory such that you can write memory reclamation code that is optimized to your particular application, leveraging information that simply isn’t available to a GC.