LED lightbanks and LED powered fresnels are on the increase, and contrary to popular belief, can and ARE being used by photographers.
I posted a thread on here a short while ago showing Vincent Peters shooting with continuous lights, it was largely ignored though as most people simply won't accept it's possible to shoot people well with continous lighting. For the record, he was using HMI fresnels and either fluoro or LED light panels, can't remember.
I spent an hour or so this morning watching a documentary on Helmut Newton, and on it, you see him and his assistants using torches and handheld mirrors. How's that for a continuous vs flash argument...!
I like both....I will use both

Of course
some people can do a good job with continuous lighting. It's the
only light source used for movies and the still photographers on the old movie sets used nothing else, and so do many of the still photographers on the current movie sets but...
1. Not all photographers are equal, and the lighting experts on movie sets are true experts.
2. The old master used whatever tools were to hand and produced what was required at the time, but not everyone wants the 1920's Hollywood glamour style now, produced by fresnel spots.
3. Film talent are able to cope with the extreme brightness and extreme heat. And their MUA had the right makeup for the job and knew how to use it.
4. The top continuous lighting gear costs an unbelievable amount of money, requires massive amounts of power and creates a very real fire risk. The junk sold on fleabay doesn't compare, except for the fire risk.
They're all tools.