The King gets the critics from animal activists and all sorts of what grabs anything just for being against something. But the annual closure of the Crown Domains predate his very life. Queen Juliana had little interest in the Crown Domains, so her daughter Princess Beatrix got a seat in the Board and practically was in charge since 1971, when the King was four years old.
So King Willem-Alexander conveniently is portrayed as a hunter wanting to shoot his Christmas dinner but the current management structures of the Crown Domain, the beheersplan (management plan), the organigram, the licenses, permissions, wild management, all predate his "rule" as Bearer of the Crown and so as manager of the Crown Domains. The management plan of the Crown Domains is in close cooperation with the State Domains and with the Province of Guelders, two other major landowners in the same region.
By hindsight Queen Wilhelmina better donated the Crown Domans to one of the Orange-Nassau family foundations instead of "to the People". King Willem-Alexander would then not have all this nosey-pokey into "his" affairs. But at the same time: the Golden State Carriage, not at all owned by the State, it's restoration paid for by the King, will probably never be used again with the same society and politicians pressing on the Cabinet.
So probably, even when the Crown Domains were not donated 'to the People' in 1956 but placed into an Orange-Nassau Family Foundation, all and everyone would blab their opinion about it as well, pressuring the King to do this or to do that.
Illustrative is that citizens of Brussels for years demand that the Royal Domain of Laeken should be opened for "the people" because they see it as unfair that one man has such a big park in densely populated Brussels. That domain was part of the Royal Donation of King Leopold II to the State, on condition of usufruct for the King. More or less the same as with Het Loo.
But that does not stop people to demand this and to demand that. That unique flora and fauna at Crown Domain Het Loo of the Royal Domain of Laeken thrive because of the serenity and lack of people, is of course easily woven away by the same 'nature / animal lovers'.