Yes, I find it interesting how princes and princesses for example in Belgium, the Netherlands, and Sweden do not normally curtsy/bow to their own kings/queens, but curtsy/bow to foreign kings and queens.
In fact, British and Danish princes/princesses are the only ones among the European reigning families who consistently bow/curtsy to their own king or queen. Members of the Spanish royal family also used to bow/curtsy to the king and queen during King Juan Carlos I's reign, but that seems to have changed under King Felipe VI.