Not to dive into politics particularly; but there are advantages and disadvantages to every form of government. What are the particular disadvantages your family dislikes? Is it the principal of it or something in particular?
One clear advantage of monarchs that I can see, are that they have an incentive to grow and expand their tax base. That typically means long-term planning (but doesn't ensure it, which is a disadvantage the UK parliamentary system seems to mitigate).
Here's an analogy: in a democracy, first-past-the-post voting is, in a vacuum, about the worst voting system that exists. But the reason that it was adopted in so many places is because it has one advantage: its sheer, utter, bone-headed simplicity. In a context where most constituents are illiterate and unfamiliar with the notion of democratic government, it behooves you to pick the simplest solution that can possibly work, even if it leads to worse results than more complex systems.
Hereditary absolute monarchy is the same thing, but for selecting heads of state. Who's in charge? The guy with the biggest army. What powers does he have? All of them. Who succeeds him when he dies? His firstborn. It's dead simple to implement, which made it an attractive solution in times before any semblance of mass communication. But in practice it means the quality of your head of state is totally detached from their actual talent at serving as head of state: the first guy in line was just good at leading an army, and the rest of his descendants are just randos who won the birth lottery. It's not a good solution unless you're willing to make loads of sacrifices in order to have the simplest system possible.
(And yes, of course, the UK is not currently an absolute monarchy, but you appeared to be asking in a general sense.)
Succession struggles were like their own whole genre of political strife until the modern era. Multiple parties can have claims of varying legitimacy -- first born might gain some advantage in being near to the previous leader, inheriting the royal rolodex and hopefully some powerful/motivated allies who want to keep the status quo, but it isn't a sure thing.
Sure, now that the top position is entirely symbolic in the vast majority of monarchies, nobody fights over it. But the if the UK Monarch was in any sense "in charge" of anything, we'd surely see the US propping up Harry and Meghan as the true legitimate heirs and we might even let them borrow a couple carriers to "persuade" Parliament of the fact. Or whatever.
Also, it's slightly bizarre that you think parliament has been "pro-economic-growth", but that hasn't been the case since the collapse of the post war consensus in 1979, when it simply became pro profit-growth.
One clear advantage of monarchs that I can see, are that they have an incentive to grow and expand their tax base. That typically means long-term planning (but doesn't ensure it, which is a disadvantage the UK parliamentary system seems to mitigate).