Which is the very reason why using 10 to 20 KHz ac current instead of 50 or 60Hz gives something like a 10% or so boost in lamp efficacy. IIRC, large department stores were one of the early adopters of using a dedicated high frequency lighting supply feed to modified luminaries.
They didn't go to the extreme of 10KHz but, afaicr, chose a common 3KHz supply generated by a Thyristor based frequency converter[1] which allowed the use of lighter more efficient inductive ballast chokes in each luminary. Nevertheless, the higher frequency supply did improve the efficacy of the tubes, reducing running costs sufficiently to justify the capital investment in the system.
[1] The Thyristor based frequency conversion technology used by such department stores required the use of a three phase supply afaicr. I suppose the less than ideal choice of 3KHz was a compromise over conversion and distribution losses that would have otherwise been incurred with a 10KHz supply.