Two different temperatures

I have read Jason's thoughts on this and I am puzzled. The accepted method seems to be to cook the higher temp more cooked meat first, then leave it in the bath and lower the temperature (with ice) and then cook the lower temp less cooked meat. Would it not be quicker (and better) to cook/tenderise both at the lower temp, remove the rarer piece and store to keep warm, then simply bring the less rare meat up to the desired temperature? It has to be quicker to bring a piece of meat from 56 deg c to 60 deg c than bringing it from fridge to 55 deg c.

If there is also tenderisation time involved the savings would be even greater. Also, no meat gets cooked for a longer time (which may affect the texture)

Thanks for any help.

Nick