Changing the seat height doesn't alter the bike's geometry. It changes the range of movement a rider has, which in turn allows more room to changes the position of the biggest, heaviest part of the bike/rider system relative to the pretty much fixed bike geometry.
Putting your seat down doesn't suddenly turn a steep head angle slack, or a high BB low. You're still not changing bike geometry, or even effective geometry. What you *are* doing is giving yourself room to move - to compensate for some of those things.
In a modern bike (say, 65-66HA, 75STA, longish reach), the bike is designed to handle most things with the rider's weight central. Dropping the seat gives a lot of room to suck up bumps, let the bike come up to you, and move forward or back as required. On a long wheel base bike, this is possible - and a great skill to have in the bag.
Using myself as an example I rarely get off the back of the bike until things get completely crazy steep or I need to lift the front for a flat drop. I'm always aiming for pretty much chin over the steerer and eyes up - a pretty committed stance. The bike handles the rest, and dropping the seat means I can let the bike move, give it the full benefit of the big springs which my legs are, in addition to the 160mm of suspension on tap.
I use my dropper every ride. I used to be a fully hardcore 'must ride everything seat up' person. Now I CBF, and just have fun. Anytime there's a descent, down it goes! Sometimes on techy climb sections, down it goes. Curiously, I'm a lot faster these days...
...I'm also gonna get a dropper for my next gen CX/commuterbeast. Just a wee one, 30mm or so.. with a hacked left hand double tap shifter to drive it.
Back on topic: for the range of bikes discussed here Just Get a Goddamn Dropper Post. Without one, you're pretty much hamstringing the machine.