The dynamics are quite complex, but essentially it's a numbers game. Introducing the delta varient into a population, even with high vaccine uptake results in significant numbers purely because even 10% of a population in the millions is alot of people who are "immunologically naive".
But your underlying assumption is right, if you have a more highly transmissible disease it will have a better chance at more infections even in areas that have historically faired better off due to controls or other reasons. However this effect has its limits - it's also kind of the entire backbone of a pandemic responce. Timing of what controls and tools you have for the most favourable outcome (which might be say, an effort to delay infections over a long period) is everything and the obvious do everything you can immediately might not be the best action to take.
