Yes, repeatedly -
1) If the monarch has a goal of "maximise my countries' power" then they want lots of trade to boost the economy, which probably implies some sort of (partially) open boarders to allow international trade.
2) If someone hates living in your country, and you don't allow them to leave, they might try to organise a rebellion.
3) If someone hates your country, they are probably not going to be the most productive citizen.
4) If the monarch dislikes some minority group, then its best to let them leave rather than persecute them, which would be likely to bring UN peacekeepers down on your head.
5) They monarch might want to attract immigration, at least from people who they believe will benefit the country, and its a lot more easy to attract people if they have the option to leave should they change their minds.
6) The monarch might actually care about the well-being of their subjects, or even of humanity in general.
There have been benevolent monarchs. There have also been sadists. In the general case I don't think monarchy is especially likely to be oppressive, but OTOH there is a single point of failure, which means that if it goes wrong it can go very, very wrong.
OTOH there is a single point of failure
There is something worse than having a single point of failure, that's having multiple points of failure in "series", for lack of a better term.
This month's media thread includes a short article on some people's idea to have Ayn Rand frozen, which ultimately didn't happen. My first reaction was a shudder. I thought, I definitely wouldn't want Ayn Rand preserved forever. My second thought was, What right do I have to say who can and who can't get frozen?
Whatever your thoughts on Ayn Rand, I think this can spark an interesting conversation: What, if anything, should humankind do about people who are widely seen as harmful for the whole? For example, if the Castro dynasty in Cuba or the Kim dynasty in North Korea decide to freeze themselves to ensure they will continue oppressing their countries forever, should that be prevented? (And yes, my opinion of Ayn Rand is such that these examples came to mind.)