Is there any reason a FLEX-6000 radio should not have DC power continuously supplied to it? Keeping the power on certainly facilitates keeping the GPSDO unit updated and ready for use when the radio is turned on.
The OCXO and TCXO will not be powered while the radio is powered-off. It was determined that both of these quickly return to their frequency and that it is unnecessary to leave these powered. The GPSDO may be optionally powered while the radio is off.
Other than for this purpose, there is no other reason to leave DC power on the radio -- it is entirely your choice whether to do so.