I don't think this is remotely true. Cars are more powerful than ever before and have way better automatic transmissions than ever before. There's simply no comparison, modern cars are faster and more responsive than older cars.
Can you give some specific examples (with model and year) where you think a modern car is less responsive than a comparable older car?
So an example is the old Renault Sport Clios. These had the 2.0 NA F4R 830 motor with cable actuated throttles. The combination of this and no turbo means the throttle response is immediate, much better than newer turbo cars with drive-by-wire throttles. In fact it's so much better than I went out and purchased one.
Power has no real correlation with throttle response. Auto boxes often make throttle response worse - in fact even the latest ZF8 gearboxes tend to have noticeable lag between applying throttle and the power to the wheels. If you want to experience this for yourself I would recommend driving a manual M235i and an auto M235i back to back.
I'd say the difference between older and newer engines is torque, I have B38 BMW engine in my car and it makes 220Nm @ 1250rpm, makes it lovely to drive around the city. Where the 172 was a bit of a pain as you had to wind it out a little to get any where quickly.
I have a 197/200, and before than owned a couple of turbo cars. I'd take the 197 - it's so much more rewarding to drive with that extra 1000RPM and that noise that comes on when the cams switch on VVT.
I've driven them all, 3 & 4 are bland compared to the 172/182, barely any faster too.