I am somebody who tends to look on the bright side of life and assume that things will work out, so if the subject of boarding came up and was relevant I probably wouldn't rush to thinking about terrible emotional damage. Here are a couple of more low key reasons why I would still go for day school:
The helicopter 24/7 argument works equally well both ways: that could also be said of a boarding school, that you are under the influence of the same people 24/7. The reason I like day school is that dc get a balance between us, teachers and friends; and I like to think we are sufficiently different to provide alternative ways of looking at life. Not the only way of doing it, but one that works for us.
I think it is useful to see how a household works on a daily basis, the little discussions had about finances and catering and who does the washing up.
Ditto to see how a marriage works close up, how we resolve our difficulties on a day to day basis, when we are not trying to be extra nice because it is the holidays. But then we have a happy marriage, might well feel different otherwise.
Dh and I have some skills which we are quite eager to pass on and which would be harder to cram into the holidays. I benefitted enormously from the discussions had around my own family table as a child, really would not have wanted to miss out on that.
More seriously, when dc have developed problems we have been there on the spot and been able to react very quickly/work with them close at hand. Also, when family trouble has struck, we have all been there to meet it together rather than having to relay information over the phone. Again, not saying it is the only way, but I think it has been beneficial for us.