Well, from what I have always read from many sources, Christmas with the Queen isn't the experience you'd normally have at xmas with your Gran. The occasion retains complete protocol, with even the private family meals having the rule that you can only eat while the Queen is eating, you may not leave the gathering to rest until the Queen goes to bed. And children are not allowed in the dining room while the adults are eating but have separate nursery area where if you don't have your own live-in nanny you brought with you (Archie's nanny is part time and will almost certainly be on xmas hols with her own family) , the children must be cared for by staff they don't know. Ok for older children but would probably make Archie quite miserable.
I do feel that if the Queen wants to ensure that her modern minimally-staffed grandchildren wish to spend xmas with her, she needs to ensure they can have a relaxing and fun time, not feel as if they are on a royal duty. If I ran my xmases that rigidly, I'd have no guests at all!!
The Queen apparently spends time with Archie regularly, as they all live nearby in Windsor. So she's not actually missing out. Prince Philip is missing out somewhat as he no longer comes South, but then I think he's so picky about who he will and won't see and under what circumstances that I don't think most of the married-ins consider it a huge loss to miss out on spending time with him! Again, his choice. He could try being more accepting if it bothered him, but I'd guess it doesn't.