I don’t really expect fancier codes to cause a huge jump in the number of logical qubits. At the end of the day, there’s some code rate (logical bits / physical bits) that makes a quantum computer work. The “FOOM” is the transition from that code rate changing from zero (lifetime of a logical bit is short) to something that is distinctly different from zero (the state lasts long enough to be useful when some credible code). Say the code rate is 0.001 when this happens. (I haven’t been in the field for a little while, but I’d expect higher because those huuuuge codes have huuuuge syndromes, which isn’t so fun. But if true topological QC ever works, it will be a different story.) The code rate is unlikely to ever be higher than 1/7 or so, and it will definitely not exceed 1. So there’s at most a factor of 1000, and probably less, to be gained by improving the code rate. This isn’t an exponential or super-exponential FOOM.

A factor of 1000 may well be the difference between destroying Shor’s-algorithm-prone cryptography and destroying it later, though.