The S terminal only has voltage to it when the engine is actually running. If the engine stalls during warm up, the alternator stops, the S terminal goes to nothing, and the choke stops opening. Those engineers back in the day were pretty smart.
If you just hook it to the ignition the choke will warm up and open regardless of the engine running or not. Key on and no start, choke will still open up. When things work right, no problem. But when things don't work, it becomes another problem to deal with. Get a winter no start, next thing that happens is the choke is also open. So now you are fighting two problems and not knowing it.
If you take a choke calibrated to warm up on stator voltage (less than 12V) and you put 12V to it, it will warm up faster. The choke will open too quick. The other way can also happen, a choke that is expecting 12V (Edelbrock) is only given 7V off the Stator post, it will warm up slower.
I like the Stator engineering solution. Even on chokes that are 12V, well the choke is on a little longer. A little extra fuel wasted. I still think it is better engineering. Says a guy that has a hand choke on every carb I have owned for the past 2 decades.