It depends I guess. Does a surgeon or anesthesiologist have to know Dutch to be successful? Or even a dentist? Btw the Netherlands has quite a few people who don't speak Dutch at all..
Well yes they do. My English is pretty decent, but I think most people would have problems having technical discussions about their health in English. Imagine a 70 year old with dementia in a nursing home. Miscommunication in healthcare costs lives.