The Queen's male grandchildren have all been photographed in kilts, just not as yet as adults.
It's false to say that the children of Queen Elizabeth's sons and daughter have shown little if any affinity with Scotland. Peter Philips (the Queen's first grandchild) played schoolboy rugby for Scotland, he was a good enough rugby player to be chosen for schoolboys international rugby tournaments, his rugby career came to an end when he damaged his knee.
Both Peter and his sister Zara were educated in Scotland, they attended Gordonstoun. Peter has attended both Western Isles cruises that the Queen has organised in the past few years.
William chose to attend an university in Scotland, even if he had intended to go to Oxbridge and didn't get in, (there is no evidence he ever even applied) there are other English universities who are just as prestigious as St Andrews eg Bristol (Where one of the Blair sons went after he wasn't accepted by Oxford) William said he deliberately chose St Andrews as he wanted to spend some time living in Scotland, he said in the future he would probably spend quite a bit of time in Wales (future Prince of Wales reference) his university years were time for him to get to know Scotland well. He spent 4 years at St Andrews and holidays regularily at Balmoral, usually Birkhall. Harry spends less time at Balmoral, he prefers to holiday in the sun.
Beatrice and Eugenie go to Balmoral each year, at times with just their father and other times when the Queen is in residence. They attended both Western Isle cruises as well.
Finally the 2 youngest grandchildren Louise and James don't get a choice, their parents spend August at Balmoral and they do too!
Just wearing a kilt doesn't mean you're Scottish, anyone can wear a kilt and not have any connection at all with Scotland! Do you expect all German men to wear Ledderhosen?
As far as supporting the Scottish rugby team, Princess Anne is the patron and she attends all the matches at Murrayfield. The royals don't double up, William is vice patron of the Welsh rugby side (the Queen in patron), Harry has just been asked to be patron of the English side.