Can't disagree with you about a decent chuck. And thanks for the attachment.
I do think a respectable supplier has the implicit responsibility that the parts supplied, chuck and arbor actually fit each other, especially if they were sold as a set. I just don't know how to provide the correct machinist terminology that says, "these don't match, and they should". To be fair, I'm working with them, but as of the moment, it's my responsibility to show that I mounted it right. I have to say, I've had to reinstall this chuck a dozen times already, because it's always loosening.
However, in the case I might be totally wrong, and my method doesn't work, I will do my due diligence and clean and fit the chuck to spec.
If they don't really fit, what is the established method to prove the degree of fit? I thought a metric might be contact area. If there is high contact area one could state the parts are matched to each other? If there was 100% contact (meaning uniform contact) that would establish best fit. (It would be a bear to separate...) 0% contact would mean there is no friction to hold anything together. Somewhere between 0 (useless) and 100 (impossible to remove) is the right answer. Is there a better or more accepted metric?