Because otherwise you'll get a whitish halo around the cutouts, particularly for dark-haired people to be pasted on black background. People's features, including but not ending with the hair lining their head, do not sort themselves into fully opaque and fully transparent pixels. While you'll usually cut out even for display on black background, if the original photograph has been cut from a black original, it will blend better.

Also you write:

My initial thinking when reading the question was that if enough light spilled on the background it would be compleatly blown out thus making the cutting out trivial.

Absolutely not. You won't be able to separate a white background by blowout behind a light blond person with "enough light spilled on the background". Any blowout background will blow out because it gets its own strong lighting: additional flashes, additional lamps. Enough light for a blowout will strengthen the halo effect.

The advantage of a blowout is that you can make it really bright while there is no way to get blacker than black, and near-black color is common. Saturated blue can be a useful cutout compromise for dark background use. Its halo artifacts at least blend better with black.

By the way: black? Are you sure you should not be having a word with the web designer? Because black is hard.