What you did is totally understandable, OP. Oxbridge freshers often get the wobblies just before "going up" simply because of early-onset imposter syndrome. It is quite correct in those cases to remind them they didn't get their place by accident, and that, since they cleared all the selection hurdles Oxbridge puts up, they are more than up to the standard academically.
Therefore, nine times out of ten, when a student with an Oxbridge place is super stressed about their first term, they just need a little more self-belief, and if this can come from the parents, so much the better.
I had the same before starting at Cambridge, yet had a great experience. My DS2 on the other hand showed no signs of freshers' jitters before starting at Cambridge some thirty years later.
No matter how he expressed his misgivings, you were not to know that it was not imposter syndrome but something more real with your DS.
Although I have personally seen how Oxbridge opens doors, I also believe in the importance of having a great time at uni, something Oxbridge students these days rarely have the time for. So yes, York will probably be right for him, as it turns out, but you were not to know this.
Finally, as has been pointed out, there's a marked difference between a first and a 2:1 these days, and the class of degree is as important as the name on the certificate. So if York means more fun and a better class of degree, in terms of his future prospects, nobody could argue with that.
Please be kinder to yourself!