That is another thing: The Queen holidays in her own country. Plus: it is an (outdated) part of the British upper class life - go shooting in the highlands (or elsewhere). The highlands (and Scotland) get recognition which is good for tourism. She makes it seem very enjoyable and it seems very British.
Spending weeks and weeks in Greek and have a permanent house gives the non-verbal message that there are better places to spend the summer than the Netherlands. For the head of state a doubtful message.
Funny thing: most Dutch agree that there are better places to spend the summer than the Netherlands.
Wilhelmina liked to travel abroad for her holidays, did not have a summer house, and only built a wooden house in the dunes close to The Hague for Juliana to play and get fresh air once the war made foreign holidays impossible. Juliana had the villa at Porto Ercole (Italy), Beatrix the villa in Tavernelle (Italy) Wax his hut in Greece (and Max a bigger place in Argentina plus a place turned into a hotel that is run by her brother).
The outrage we're currently showing has nothing to do with their houses abroad, but is basically jealousy: You are one of us, no better than the rest of us, we have to stay home or holiday in The Netherlands, you have to set an example, we stay home, you stay home. We pay, you play (according to the same rules that we do, but then again we're flauting those rules by the thousands, flying or driving to places that will still allow Dutch tourists like Austria and Dutch Caribbean much like we flaunt the rules of social distancing and no gatherings of more than 4 and that's why whe have a huge number of positive tests everyday but hey, we're healthy and not old so we won't die).
Mind you, I think it was very unwise of them to go, and also that PM Ruttte sucks up to him too much.