This is something I've been doing a lot of reading on lately, and I'd agree that the mowing does help on multiple fronts based on both what I've read as well as the experience of mowing my own pasture the last few years.
From what I've read, I'm coming to the conclusion that rotational grazing is probably the single best method of managing a pasture in order to keep the grass between 4" and the height where it goes to seed. However, if the animals aren't doing it then helping out with a mower can be very useful. It seems that many pasture grasses don't handle being shorter than 4"-ish tall too well. Then on the other end of the spectrum when they get to the point where they are developing seed heads they're putting more energy into developing the seeds rather than growing vegetation. So if they can be kept between 4" and the seed development height they put more energy into growing the plant's vegetation (which keeps it tender/fresh and higher in protein).
As others noted, and I've seen on my own small place over the last couple years, mowing also helps reduce the amount of weeds that the animals won't eat as it will keep them from going to seed..... and depending on the type of grass, the grass may also start to spread by means other than by spreading seed (some of the areas I've been mowing have gotten noticeably thicker grass in the last couple years ...in addition to having fewer weeds).