@AmigaCloneI suppose it depends on how you define "coming of age." Does one define it strictly in terms of reaching the age of majority, in which case 17/18 would be too old, or does one define it as a period of significant personal growth and development, in which case, that phase from about 18 through to mid-twenties is arguably when people undergo the most essential changes, transitioning from a protected (in many ways) adolescent/young adult into fully fledged adulthood.
Personally, the period I spent at university was when I noticed the most significant change in myself. I was a completely different person after just one term in Aberystwyth than I was before I arrived. By the end of my three years in Aber and one year in Swansea, I was much more self-sufficient, politically aware, and prepared for what lay ahead than I was after my A-levels. I was a boy when I left home to go to Uni. After graduation, I was a man. I felt, in myself, far different at 22 compared to 18, than I did at 18 compared to 14.
Maybe I'm an outlier. I don't know. That's just my personal experience. But I will say that I've seen a similar significant change in my son after his first year at university compared to, say, the period between his GCSES at 16 and his A-Levels at 18. He's more mature, more confident, and more aware of the world around him. I'm fortunate that we've always had a good relationship and have frank and open conversations about all sorts of things, but our discussions are now far more "grown up" than they were even this time last year.