That may have been true in the "old days". I am not certain it is true today. In the old days it was pump the gas peddle and turn the ignition. Now, with computer technology and fuel injection they can start the car with only an idle mixture which is clearly a save. How much of a save? If it is just stop and go traffic, or a stop sign, or stop light, I can't imagine it is a significant saving, although with 100 million cars on the road, maybe it adds up to something. I would guess the same is true with emissions although it depends on how efficient the initial ignition is.
I think the stop/restart feature really stresses the starter motor and battery. It could also stress other parts that come to a stop and then restart. I hate the feature, although I don't have it in my car. I suspect if I buy a new car I may have to deal with it. It reminds me of the feature some manufacturers put in their cares in the 1970s where you have to engage the seatbelt of the car wouldn't start. I think some companies also put governors on their cars to prevent them from going faster than 65 MPH. These are annoyances that address minor problems.