We don’t need exponentially more physical qubits because we have quantum error correction schemes that exponentially decrease the logical error rate with only a polynomial increase in the number of qubits. There are in fact many schemes for this (https://errorcorrectionzoo.org/) with the surface code mentioned in the blog being a leading approach.

Details for how this could work for factoring are here: https://arxiv.org/abs/1905.09749

There will be engineering challenges to scale up these implementations but in principal you shouldn’t need exponential resources (unless there is something wrong with quantum mechanics). This sort of error correction scaling does not exist, for example, for analog computing.