As far as royalty is concerned, if the majority of the people of a given nation with a monarchy feel that it functions well as a focus of a sense of history, tradition, and national identity, that's a sufficient level of "relevance". It's their business.
Most hereditary aristocrats these days are involved with their own concerns and problems, like everyone else, so the issue of "relevance" isn't applicable. Even in the UK, they don't serve in Lords unless elected by members to do so. The majority of Lords members are life peers. Aristocrats manage their estates, if they still have them, or they work in normal careers. If titles were abolished, their lives wouldn't otherwise change. They'd keep whatever property and careers they had.