I disagree completely that they're potentially worthless experiences geared only for the 1 in N who embrace the subject. The content of the material is in many cases mostly irrelevant - it's the fundamentals behind that content that matters. Claiming that it 'doesn't matter' because you don't actively utilise it in your job later on misses the point entirely. For example:
Maths - teaches logic and critical analysis of problems. No one cares if you don't remember SOHCAHTOA or the like. If you can think about using knowns to resolve an unknown, you've got the main thrust of maths classes as they stand for non-Engineering, non-Science people.
Physical Ed - teaches healthy habits, ideally. No one cares if you remember the rules to field hockey or rugby or learn to run faster. The idea is that you learn/are exposed to healthy exercise habits and (ideally) healthy nutrition/etc. if it includes that too.
Music - teaches quite similar stuff to maths, in fact. No one cares if you can't re-draw the circle of fifths, however understanding the patterns in music and why they exist (e.g.: why you don't tie the 2nd and 3rd beats of the 4/4 time signature) gives you insight in to the mathematical underpinnings of music and lets you appreciate it more to boot. Not to mention playing music engages and assists the brain areas used at maths, problem solving, etc.
Art - You learn to understand and appreciate design better. You learn to appreciate culture. No one cares if you can't remember what primary colours to blend to produce a certain new colour, but understanding the role of shadows for contrast, or vertical lines in e.g.: paintings of architecture, help you appreciate the world around you.
Science - Again like maths, logical intuition and problem solving. e.g.: for physics, no one cares that you can't recite the equations of linear motion, but understanding why something goes up and then falls down, intuitively, is a good way to teach critical analysis of problems.
The second benefit of all of this is that you then also get exposed to this content, which means you get a general introduction to those fields. As you say, it helps bring the fruit to bear whereby people find out they enjoy/have talent in something, but additionally it means that because you sat through music in school you probably at least understand why some songs sound sad (minor scales) and others sound happy (major scales) so you can appreciate it more.
I absolutely agree with you that programming should be in there. Again, it's not about learning how to declare variables in python in particular, but rather about the logical underpinnings of code structure and understanding how that all works. The benefit isn't going to be that 100% of kids can read some javascript dump and work out why the webpage doesn't load properly. It'll be that when they're sitting down in excel and they're trying to assemble that data their boss wants in a particular way, they'll be more capable of logically stepping through each component step of the equations required and understanding exactly how it must be built up to produce the result they're after.