I agree that using a DSL isn't an automatic thing. However, I think there would be an equal number of counter-examples - cases where a problem has been shoe-ho

I agree that using a DSL isn't an automatic thing. However, I think there would be an equal number of counter-examples - cases where a problem has been shoe-horned into an existing language to the point that it become illegible. (In fact, you could argue this happens more often than not).