I would start by saying modern royals derive a certain amount of legitimacy from being less important. People generally dislike the idea of royal exercising major regular power, it makes them more dictatorial and undemocratic, so the remaining European monarchies have moderates themselves to whatever lower level of influence people found acceptable in order to survive. On the converse side, outward-facing PR is more important than ever because what influence and prestige they retain is now even more visible and more scrutinised than before.

It's important to understand the full history of monarchal evolution. Early Medieval monarchs were always much different from their nobles. Early Medieval monarchs built their power mainly off social status and forces of arms. Which could be pretty powerful, but was limiting, particularly in its range and sophistication. Which was why institutions from early on started to become more complex, and why early medieval monarchs (at least in my knowledge of England) were very itinerant, travelling not only between palaces but also performing travelling court sessions all over the country which were the predecessor of the modern localised static courtroom (hence the name).

What happened in the Early Modern, in terms of the most important singular development, was the use of the court space as a way to further the control of local nobles. While there were significant development in institutions towards modern complexity and efficiency, and in some cases increases in the personal powers of monarchs themselves, they were still quite reliant on local nobles. So they used the court space as a way to get local elites on board. Early Modern princely courts became increasingly spaces of display, of patronage for arts and sciences, of financial and political opportunities, and an obligatory part of noble social life. Early Modern courts actually became less itinerant, instead, while they might move between residences the main objective was to get people to come to them. In England, the court justice system had replaced any royal travelling sessions, with travelling justice also being administered by judges and magistrates the same way as the sedentary courts. The most dramatic example of Early Modern court centrism, and arguably one of the most personally-powerful monarchs of all time, was Louis XIV "the sun king". Under his rule was Versailles was a dense social space which intricate routines that everyone memorised.

But of course, the use of the court space as a social centre relied on its usefulness to those who came there. In offered offices, money, lands, a chance to take part in lavish living, and access to a network of other powerful people. When later Early Modern monarchs started to decline in power in the late 17th and the 18th century in favour of parliaments and capital business, the attraction of court spaces slowly began to diminish. While court posts or regular visits remained a feature of political life well into the 19th century, they became increasingly less central to the distribution of power where monarchies were declining. Even in monarchies like the new Germany or Russia where they were stronger, reforms had to be made, and professional modern bureaucracy, legal systems and militaries were less reliant on the aristocracy, although aristocrats still played a major role in them.

Increasingly, with the growth and democratic government and professional non-inherited government, one of the key ways to make monarchy legitimate was to make it less obstructive to these things, as it turned out they were generally more popular. Over time there was simply less appetite, and less tolerance, for monarchs acting as vigorous individual governors. In modern Western constitutional monarchies of course, the primary role of governance is taken by Prime Ministers and their professional government, which are composed exclusively of elected figures or appointed bureaucrats. In such a system, any too-conspicuous intervention by ancient hereditary monarchs is going to be controversial, such as the 1975 dismissal of Australian Prime Minister Whitlam, which was controversial even though it was an intermediary not the Queen. The fact that information them came out suggesting people at Buckingham Palace (her secretary and Prince Charles) where involved with Kerr's (the intermediary) decision only revived criticism. No-one expects Elizabeth II to be very political. Any suggestion of monarchal or court intervention is perceived as a potential threat to democracy. The modern Western monarch is there ironically most legitimate when their legitimacy is less relevant. They have no real argument for a major role in political power that would be broadly accepted. So they must be perceived to "embody" the state in a general sense.

The converse of this is the social role is even greater. The palaces themselves are actually more private than they were before, with less of a complex social network. But modern constitutional monarchs spend a lot of time on PR for the broader public, which was previously much less important than the court circle. So some aspects of ceremony are almost more rigid and arranged. The British monarchy has also made more of a habit of actually visiting foreign colonies since the 20th century, even Queen Victoria who was already mostly constitutional never visited Africa or Australia, whereas Elizabeth II has a number of times. The ceremonial public celebrity role has become the dominant one. Queen Victoria played into this role by presenting herself as the ideal Victorian woman, a good Christian housewife, which was in specific contrast to her being a ruling queen. Elizabeth II's public presentation is largely the same.