Lets take a real world example: China.
The communist government forced a new dialect (Mandarin) on the people. Note that they did not in any way prohibit the old dialects, just mandated that the schools teach the new one. (The schools may also teach the old one.)
We are not quite a lifetime from that decision but the people from before the schools changed over are retirees, not active in the business world.
I have a grand-niece over there growing up in a major urban area, there are two dialects spoken in her area, the mandated one and the local one. She has no surviving relatives that only speak the local dialect. If she walks into a business everyone will speak the mandated one. By the time she's in the labor force there will be very few customers who don't speak the mandated one. (Note: The written language is the same, those few customers can be handled with pen and paper or even simply writing on your hand with your finger.) Why should she waste her time learning the local one? The only benefit it would be to her is so her elders can't talk past her by using the local dialect and even that might not work because many of them also speak nearby local dialects.
There no doubt still are some who learn the local dialect also to communicate with elderly relatives but that won't last much longer. Within 10 years I would expect the rate of learning the local dialect to drop to zero. A lifetime past that and the local dialect will have joined the dodo.
Now, in areas with poor education this process will take longer. I've seen my wife struggle with people from a rural background, their knowledge of the enforced dialect is often incomplete and their local dialect is a different one, thus leaving the written form as the only one they truly have in common.
Note that this switchover is only happening because the new dialect is superior to the old--everyone speaks it rather than only people from your own city or area. Despite speaking several local dialects my wife's knowledge runs out within 200 miles of her hometown, beyond that it's the enforced one only.