I think it should be s mix. I'm from Wales not England but presume you mean the UK as a whole. I chose my a levels mainly on what interested me - English, welshi, history and RE. Incidentally, I never did well at the sciences and maths - subjects I hated, couldn't 'get' and barely scraped a pass. I passed my maths GCSE finally aged 21. That was only because most places want a c in maths, there was certainly no desire to learn that!
However I do think my good grades in the subjects I enjoyed were linked to the fact that I liked them. History in particular. I really enjoyed it and enjoyed lessons so I did well, it helps when you have a teacher who makes the lessons fun too.
Although let's be honest, learning for learnings sake, won't get you a job. Id have loved to not have done science, it or maths in school. But my chances of getting into uni and then getting a job, would be crap.
Children shouldn't just be allowed to do only the subjects they enjoy. They might do better in them, but ultimately school and learning isn't just for enjoyment. Enjoyment is an important part and you'll do better if you enjoy school, but the goal of school is to pass qualifications that allow you to progress in your chosen career, to be literate so that you can find a job etc. Letting. Child who only likes PE to just do PE, is doing them a disadvantage.
So I don't see the problem in focusing education on getting qualifications and a good job. In fact it's probably a good incentive for teenagers who don't want to revise. Telling them they might enjoy doing English might not help, but giving a sharp reminder that unless they do get some qualifications they might well struggle financially or not go into their chosen job, is much more of an incentive.
Yes it should be enjoyable where possible. But the basic aim of giving children an education is to enable them to progress in life.