Many students have an interest and want to pursue it. It's only through self-motivation that people really learn.
There was a study of where hockey players come from, they tend to come from cities of approx. 50,000 people. Large enough for schools to offer many different types of programs in schools, but small enough that a teacher knows each student and their family, and can help a motivated student train. In many large urban centers teachers don't live in the same communities that their students are from, and can't offer that extra oversight. This is why in large urban centers, it would be better to start to specialize early.
All roads lead to the same destination. Eventually you'll need to know a bit of history, math, etc. no matter where you start from. So beginning in a specialization doesn't exclude other knowledge.
Sometimes it's better to have an in-depth knowledge of one subject, if a student starts early and focuses on one thing, they'll be ahead of their peers.
Knowing Latin doesn't compensate for lacking knowledge about the fundamental details of the world we live in and share.
> The point of a fixed curriculum is that there is a minimal level of knowledge on various subjects that we should expect all of our fellow citizens to have.
Do they actually have it? Do you think schools that have fixed a fixed curriculum are successful at teaching this to everyone? Try picking some average people and asking them to explain Boyles Law, or why and how Rome became an Empire or the causes of the Second World War.
Is the level of minimal knowledge the same for everyone regardless of talents? Some kids will know before they are teenagers than most adults ever will about any of the topics picked, and many more.
I am confused about why you think knowing Latin somehow excludes knowing history of physics or biology.
You are arguing from a position of not having an experience of eduction outside the school classroom setting. I am speaking from experience and from having actually read up on the evidence.