I don't think that the purchase of new diadems would be 'politically unpopular'. The politicians and the public are barely aware at all about the family jewels. Queen Máxima has worn some eyecatching pieces in the public eye and it has never caused any criticism. Three members of the Royal House receive an annual income from the State. Besides the personal income (the A-component) which is really personal and of none's business how it is used, there is also an additional income (the B-component) to cover functional costs.
For the functional costs: the King has a budget of around USD 6,150,500, Queen Máxima has a budget of around USD 801,000 and Princess Beatrix has a budget of around USD 1,320,000.
When Queen Máxima decides to purchase a set of jewels instead of gowns, hats, gloves and accessoires, because she sees this purchase as necessary "in the exercise of the royal function", then she can do so. Whether she does it from the A-component (personal income) or the B-component (functional costs) would be a matter of discussion with the King's Treasurer but in essence, when the Queen buys a new set of jewels, so be it. For so far I have not heard politicians questioning the jewels of the Queen.