Totally agree Ajax about your thoughts here, i've been using this method and all the others for years and it really does work on the right job.
As i say you don't just spray it, it needs to be worked in so you can do that as you cut in. Obviously you can't use it in someones new kitchen!! But then primer on rollers, sponges and brushes aren't the most splash free method either.
I use a hand sprayer or the larger pump sprayer (green ones £15 B&Q) for big floors.
But some things have to be rolled or sponged, ie Mape Ecoprim grip etc.
I could be very wrong, but with a sprayer you could spray on to anhydrite for example a light coat, then back roller it, this way you can control how much is being applied, with a roller or a brush, you tend to slap a big dollop on and then push it around, which in my opinion could over saturate the substrate. If the floor looks like it needs some more priming, its very easy to do again, you can do it standing up and it gets done much quicker.
I would not advocate theuse of sprayed primer on low laitance type anhydrite as this has generally a very low porosity to its surface.if you are prepared to sand the heck out of it to get a porous surface then maybe. On the older style anhydrite screeds which form some laitance then as long as the laitance is removed the surface is generally much more porous so maybe... My honest answer though is that I don't know because I have never done it.
As for standing up.... A ceiling roller with a 9" or even a 12" sleeve for really big areas and a roller tray or better still a pumped roller would save you loads of time, have you standing up and would work the primer into the screed....
however if it works for you ..... Go for it