We are expats and moving regularly is a lot, especially on young teens, Our kids at different (teens) times thought they wanted to go to boarding school rather than move country every two to three years, We looked at boarding schools in both the UK and in Switzerland, but they both finally decided against it. In the end we decided to be a commuting family, mainly for the older ones' final three years of school, which means the younger one gets a 5 year stretch in the same school. Husband is based overseas and spends one week a month at home with us, although it doesn't always work out. It's a difficult family dynamic to manage, we all miss him and he misses home life, but it is the sacrifice we agreed on for some stability in the kids education.
I do think 11 is very young though, would never have considered that age, but I kind of understand why some families go down that route. We have friends whose 3 kids all went to the same boarding school, two of the kids loved every second of it, the 3rd one has said it ruined his life. It really is down to the personality of the kids and also how close the family unit is, whether it is a big wrench or not to move out of the family environment.
I am sure it is reassuring for you and your husband that your kids are thriving, not all overseas schools provide the equivalent education they would get in a top school in the UK..