It is an interesting point, which seems to undermine the entire foundation of hereditary monarchy. I mean, originally a person was deemed acceptable as a monarch, a consort, or even a peer of the realm on account of blood. Bloodlines and breeding were the sole basis used to determine a person's worthiness to hold a crown, a title or an office. Granted, in those days when few people were educated (or even literate), a person's bloodline was virtually synonymous with their level of education and thus their worthiness to rule or govern.
Throughout the 20th century, the entire concept of "blue blood" has been watered down to the point where it is meaningless - the number of people remaining today who can claim pure noble blood (descended solely from ennobled families on both sides down through many generations) is growing smaller and smaller.
On the one hand, this is essential for the survival of the institution of monarchy in modern times; people today would certainly be less likely to support a monarchist system if it remained the closed circle it once was (allowing only intermarriages between noble houses). On the other hand, it becomes harder to justify a hereditary system at all if anybody can join.