I don't care how much "real" power they have. If you actually believe in a meritocracy how can you defend someone getting a job because of their lineage, attending real political events and ceremonies and influencing policies that way? And let's not forget that in many cases, they ACTUALLY have institutional powers they just don't use because they don't have to, the institutions serve their interests all the same.
Sorry for the pointless rant. It just happens way too often.
I live in a country with a monarchy, we are conditioned from a young age to respect them through both school and the media. It is instilled from childhood and habits that are so longlasting are incredibly hard to break. Even though I started to move towards leftism as a teen it still took me another good few years to properly realise how fucked the monarchy was.