Most clinical laboratories would have 10 to 50 PCR instruments that they can use to run the initial amplification reaction in parallel before Sanger sequencing. Also, Sanger sequencing uses a plate feeder, so you can add new plates on top as the second round of PCR reactions finish.
But, more importantly, the qSanger can by-pass RNA extraction, which seems to be an important bottleneck in the RT-qPCR workflow.