The main arguments against continuous lighting were always:
They get hot
The colour balance is "wrong) - ie too yellow
The bulbs didn't last very long
have a look on ebay - modern continuous lights are daylight balanced, energy saving, cool running, and the bulbs last about 10,000 hours.
They are more predictable than flash, do not require a flash meter, and can be usaed with any camera - no need for connecting cables from camera to lights and no need for infra-red / radio triggers - can also be used for video - all in all, a good choice I think