Maybe go home from work tonight and explain it as even handedly as you can and see their reaction? Or would you just not, just in case they saw it as an opportunity to get some real independence, whilst knowing that they had you at home forever and always but that you were just helping them live their life and find their feet?
You are coming from a place of believing that sending your kids to board is a 'good thing' and that kids who don't (or can't, due to finances, after all the outcome is the same) are 'missing out'. That for those that could, it's a choice to be made.
For us, boarding is an alien concept. Which I'm pleased about tbh. I would never send my dc anywhere to board so they'd never get the choice...but I can imagine the reactions of my teen dc if I floated the idea. Like I said, it's an alien concept to us. It would be akin to me asking them if they'd like to move to [random village] 100 miles away. Or maybe, shall we take up crochet as a whole family hobby? Or one of a hundred other, totally random pointless undesirable suggestions. It would be 'Whaaatttt? Why?'.
My eldest dc (16 and 13) go to the best (state) school in the County. They have a huge range of hobbies and extra curriculars, both in and out of school. They're excelling in pretty much everything, are happy well adjusted kids with their own bedrooms, plenty of freedom and independence but within boundaries appropriate for their ages. They get dinner with the family most evenings and plenty of alone time, if/when that's what they want.
They don't need 'real independence' and to 'find their feet' away from home. They can do that at Uni, and plan to.
They're not coasting, dreaming of a better life and opportunities and pining to go somewhere else to spread their wings right now 😂. They're children, living their best lives already, making plans for the near and distant future.
Boarding doesn't figure for us.