It is perfectly possible to leave school with little to no MFL: dh and his brothers, my daughter and her cousins are a few examples. (It does not fare much better in Italy)
I was brought up abroad and like you I was shocked by the gaps in the education system my dd went through.
sometimes being forced to learn something introduces you to other whole realms. I never had to force ds to learn anything, he was and is introduced to all other realms because he is, always has been, curious and I research/ed and provide/d materials, books, excursions, answers, discussions; I expose to new ideas, concepts, topics, activities... I didn't have to force music either, ds asked to learn guitar, I found a suitable teacher. (dd had little music exposure at school but enjoyed the piano lessons she asked for and we paid for)
Also with Maths, I would never have had the patience to plough through trigonometry or sequences alone. I needed the help that teaching brings
He would be the same, that's where I come in. I explain to him, I show him a couple of examples, I guide him through a couple more and I'm still there until he's fully confident. He also has access to mutiple resources, internet included (such as conquermaths and learnerscloud)
I do think you need to be made to do the things you don't like doing though, not just let learning go where you are interested in.
He does! He still has to do homework: how would he pass his exams without practice?! He is also responsable for cleaning his room, putting his own clothes away, tidying after himself, helping with the dishes and cooking, helping with feeding the dog, chickens and fish; being on desk, drill and clean-ship at cadets and various other 'boring and dull bits'. I almost forgot the most diificult part for a teenager: he still has to set an alarm, get up, feed himself some breakfast, have a wash and be 9 o'clock sharp at the table and have a hair cut.