Rule3
Grossly overused instruction
that means 
nothing.
disagree with you there I'm afraid, at least if the ATCO is any way half capable.
A/C will climb at the best rate for them - i.e. a balance between climb performance and economy.
ATCO climbs A/C to a safe seperated level from conflicting traffic and monitors the climb rate, bearing in mind the statement above.
ATCO, using judgement and experience (it's what we are paid for after all), decides that a climb through will work at the current or slightly better rate than is being shown at the moment.
ATCO instucts the A/C to climb, using expedite through a few critical thousand feet to ensure that the situation works. The word expedite means forget economy, give me performance. It should be used for a level band of a few thousand feet, not for tens of thousands.
Not a useless technique, but one used in busy airspace everyday - though used sensibly when the situation dictates.
An
extremely valid technique and instruction which if used in the correct instances, will help greatly reduce ATCO and sector workload/complexity.
CAUCATC
As
rule3 correctly states in his first answwer to you, the ROC could be anything - it depends on the aircraft characteristics etc.
As an ATCO, you are paid to use your judgement, as I have explained above.
If you are in a situation where you want a specific minimum ROC to ensure that a situation will work, then you can ask the pilot if they are able to give you that rate or you can specify it in the instruction - the pilot must tell you if they cannot comply with the climb rate if you use the latter technique - and as it is part of (a
condition of) the clearance, they must tell you so without starting the climb through.
ZKDLI
That reference you have given is amusing - it states 'must climb/descend at best rate', but it does not state that by best rate it means best climb/descent rate... a best rate for a pilot could be the most economical one, though in the context of the definition, you would hope that the pilot understood that in this circumstance, 'best rate' related to best ROD/ROC!!