Now I've tried to write a little text about health and how to talk about it with children, more times than is probably healthy (tihi).
So no - I ignore common sense and put it this way:
Be healthy, teach the children about nutrition and exercise - but do it with love! Let them try and marvel at flavors from around the world (sweet and salty and everything in between) and move together (go for a walk, build an obstacle course out in the yard, jump in bed, do yoga together in the evening in front of YouTube - whatever).
Also, be "unhealthy" - break the rules. No one dies if the candy is eaten on a Tuesday and not a Saturday. Maybe it was the healthiest choice you made that week. Because you needed it and because you laughed more than in a long time, all evening. Remove screens and mirrors for a moment and dance with your WHOLE body and WHOLE heart.
Regardless - throw out the "old teaching" of two sad boring little vegetables (per meal) that EVERYONE still hates but "must eat or there will be no Saturday treat" to hell (quite literally). Compulsion and food anxiety have never created a healthy attitude towards either food or exercise, have they?
I am by no means a professional here, but with the above as a basis, maybe the conversations are a little bit easier when the children get older and the teenage years slowly enter? Because the world outside is brutal. The image of health is sick. The ideals impossible to escape. The children need a solid foundation to stand on to at least have a chance to tackle it!
Health is what we give them, every day, all the time, isn't it? (Not the sad vegetables and anxiety over being tired of football practice).