I think a three week separation is doable, and then there are half terms and holidays; and the holidays are long. You can also talk every day, and if possible, get to matches and things at weekends, so you see the dcs then. My dh's boss and his wife do this, and it works well for them and their kids.
When ds was at prep, and I was teaching, I dropped him off at 0750, picked him up at 1900 after prep, and there was Saturday school as well, so Sunday and 90 minutes in the evening was all I saw him for. He had exeats, and long holidays, where I got to spend time with him. Had he boarded there, I could have gone up to see him every day, as it was, we only saw each other for 2 hours a day in reality and Sunday. Boarding would not have made a huge amount of difference, apart from the commute I had to drop off, then get to my school, and reversing the process in the evening.
My dh did more canoeing, climbing and swimming than he ever would have done at home; and my nephew is doing more after school things as a boarder than are available at the local comp, and given his mum's nursing shifts and my dbs long hours.
You totally ignore of course the impact on the child of the parents divorcing and their home disappearing altogether. If a couple have kids, then obviously it's the whole family that are split, not just the parents. My Dad told me I was at fault for his adultery and if my parents separated and divorced, it would have been because I didn't go to boarding school, and my Mum didn't move with him as I went to comp. They eventually divorced when I was 24, and I still feel guilty at 42.
I think you are being a bit naive in thinking that parents don't discuss the boarding option with their dcs. I certainly have with mine, and explained why we are considering it as an option. Just because you are anti boarding doesn't mean that those of us who can see the advantages are unloving, draconian or lacking in communication skills.