In any case, you'll be streets ahead of most 17 year olds in the job market simply by turning up to interviews on time, speaking in complete sentences and not interrupting the conversation to answer your mobile phone.
Are you discriminating against 17-year olds now?
That said, I remember being younger than the OP and trying to get an apprenticeship (not as a plumber) with a man who had it in his head that he was thinking of a 16 year-old (I was 25). I explained I understood the funding circumstances and, well, basically was he intending to pay the apprentice anything more than what he was getting from the government?
My outgoings were, then, minimal, and Iexplained that I could have taken a dramatic pay cut to make myself employable as an apprentice as I didn't want to spend all my life being a cleaner. He said, oh yes, I was planning to pay, and I said, well, then please don't write me off, and if you think I'm worth interviewing apart from that then please do call me. He said he wasn't thinking of taking an apprentice until the next year (obviously nonsense - as he was advertising). I never heard back, but then it was fairly obvious just from that conversation that we wouldn't have got along. I'd been debating things with my teachers since the day I started school and so I probably wasn't his type, nor he mine.
Problem with apprenticeships is that a lot of organisations are happy to take on an apprentice for a year and the next year replace them with another 'apprentice' to keep getting the funding and to keep down costs. Apprentice receptionist anyone? Schools have been known to do that with their learning support assistants so while it may be true that it is harder to get an apprenticeship if you're older, I suspect plumbing is a bit different because no one wants an apprentice plumber just for the year anyway.
I never got a formal apprenticeship because I'm too weird and difficult, but I'll get my plumbing business to work out in the end, so don't give up.