I cannot vouch for the capability for the 737 to autoland on one auto pilot, but I would be very surprised if were certificated to do so.
You don't need to be surprised. The fact it's not certificated to do so, everybody knows.
Deficiencies in how knowledge is used and in particularly about making assumptions?
Making assumptions is the only thing we can do over these grounds, until somebody actually tries in the airplane.
Yes,
here we are pushing our mind beyond the strict limits of functioning like robots, the anal behaviour you must certainly love.