There are several properties that separate real quantum computers from the "BQP machine," including decoherence and SNR. Error-correction of qubits is mainly aimed at decoherence, but I'm not sure it really improves SNR of gates on logical qubits. SNR dictates how precisely you can manipulate the signal (these are a sort of weird kind of analog computer), and the QFTs involved in Shor's algorithm need some very precise rotations of qubits. Noise in the operation creates an error in that rotation angle. If your rotation is bad to begin with, I'm not sure the error correction actually helps.