I don't think they'll achieve an outright ban, but we probably will see a limit on capacity for ICE engines, and see them disallowed in trucks and other heavy vehicles - they account for a majority of emissions.
Market demand will take care of the rest, as I don't think there'll be much interest in new fossil cars once electric is cheaper and more powerful, which is happening as we speak.
Also, VW probably achieved a stonking own goal with the emissions scandal - many who bought "eco" cars thinking they were doing their bit have been let down, and the Germans are an environmentally conscious lot.
Me, I've been putting my money where my mouth is and buying nice houses on busy noisy roads. They'll still be busy in ten years, but quiet and no longer polluted - and once driverless tech is firmly in, congestion and density go away too.
My estimates for the velocity where tire noise will be substantially louder than the rest of the car are much higher, more like 60km/h.
[1] shows on page 3 a significantly higher tire noise for 50 kph (+8 dbA) but doesn't show lower speeds than 50 kph.
[2] is in German and from the Austrian Federal Environment Agency and states that for cars build after 1996 25 kph is the point where the tire noise takes over at a steady speed and at 50 kph when the car is accelerating.
1: http://www.asphaltroads.org/assets/_control/content/files/an...
2: http://www.umweltbundesamt.at/umweltsituation/laerm/laermsch...
One other thing that came to my mind is that tire noise is usually concetrated in the high frequencies, whereas some cars, especially trucks, emit very low-frequency noises. The latter penetrate walls and windows much more easily.
Of course tire noise won't go away with electric cars, but in my opion there's a vast underestimation of how much quieter roads and cities could be without combustion engines.
Also, with truly autonomous vehicles, travel speed would likely be increased in order to maximize capacity - like it's done with trains, where both speed and minimum distance are chosen for maximum capacity.
And energy efficiency decreases with higher speeds due to air resistance, so saving energy (reducing load on the grid from charging) is also a competing concern.
Also, tyre noise is high frequency, easily blocked by windows and walls. Engine noise is low frequency, and makes your dishes rattle in the cupboard.
Either way, no skin off my nose, the fewer agree with me the lower these properties are priced.
A century and a bit ago living on the bank of a canal would have been seen as madness. Now it's desirable.
I think there is a good chance this could be reached unless the auto lobby does not come and plays spoil sport.
The German gov't also subsidised the renewal of older cars in 2009 with 2500€ per citizen, so that's another model that could be of interest to lobbyists. https://de.wikipedia.org/wiki/Umweltprämie
Of course, that won't work out for the German industry if everyone buys a Tesla.