This question should be addressed to your manufacturer.
There are no right or wrong answer,
Vendors and other end users not necessarily consider 650 F as general service as yours, there are also other factors
Data provided is not complete enough to be assessed.
What is the Gate valve type (double expanding, wedge, slab,)? Size and Class? Service? and most important, under what condition you will operate the Valve?
Have all of us experience Gate valves stuck Close / Open? I believe the answer is Yes
Why? My personal experiences there are three factors: 1. Scaling built up (stick / stuck) ; 2. Long time in Fully close / fully Open position ; 3. Plant/operator retract (Open) the Gate valve at full DP and high temperature
Let's now focus on point 3, it is due to thermal expansion of the wedge against seat (in combination with full DP, pressing the wedge against the seat at one side).
Not my nature to guess, however I presume that the manufacturer have experience this before. And since they cannot 'articulate' the end user operation protocol, they put their own precaution.
For instance Class 600#, Design temperature 450 deg Celcius. It may perceived by some end user that they can Operate the valve from fully close at 450 deg Celcius and 70 barg or more (its within the valve design Temperature & Pressure). And there is a high possibility it may be stuck during the attempt.
Therefore, the solution is, manufacturer put safety notice which allows the valve to be cool down first (down to max e.g. 650 F) prior any Operation.
As for your other example, Check and Globe valves. They both have different failure modes compare to Gate (seldom stock close, unless pin or stem broken).
Regards,
MR
Greenfield and Brownfield have one thing in common; Valve(s) is deemed to "run to fail" earlier shall compared to other equipments