Why would a photographer use a single head 1200 W∙s flash?

I am not sure which direction your question aims at, but as a use-case for a single head high-power strobe, photos in bright daylight come to mind.

In certain scenarios using a flash to provide fill in shots against the sun, especially if you want to use a large softbox or reflex dish, you will need all the power you can get.

Also if you need to use HSS to balance ambient light in bright light with open aperture, the available power will get reduced greatly. A 600 W∙s strobe might then already be too low in output for outdoor shooting. So you have some extra wiggling space regarding power. You could of course circumvent this scenario by use of an ND filter.

The Godox AD1200 is a really different type of light than your Dynalite setup.

First off, it's a Li-ion battery-powered monolight, not an AC-powered pack and heads. No cables at all. So, it's really easy to take out on location, where you may need more power coming from a single head to balance against sunlight. It's also HSS and TTL capable. And having more power makes HSS for daylight fill more usable, as well as simply letting you recycle faster with lower power settings if you need to (its minimum power setting is 1/256 power).

And more power is better for bigger spread or larger distances between the light and the subject (say, for group shots or very large subjects).

In short, it's better for location shooters than a studio pack'n'head setup would be.

And Godox now also makes the P2400, a 2400 W∙s pack that can take two heads if you need that type of power for shooting, say, really big products, like cars.

See also the suspiciously similar question :) at: https://www.dpreview.com/forums/thread/4467769

Some photographers (not me, so I cannot give more details) like to work with various traditional film/plate processes, which have extremely low ISO values and need ludicrous amounts of illumination to avoid motion blur with many subjects. I have seen these people preferring such powerful monolights. Using a single head is likely simply due to space or setup complexity constraints....