DS1 was in the same boat, he didn't want braces and accepted that in future if he wished he'd had them he would have to pay himself.
DD & DS2 both qualify for NHS and its a massive job, requiring a huge amount of commitment from them to clean their teeth properly, lots of appointments and having to take extra precautions during PE etc. DS has had to have teeth extracted, DD is currently battling with twin block appliances which affect her speech and therefore her confidence.
I certainly wouldn't have wanted to force them into doing it against their will, especially the extraction
. We discussed the ins and outs and they both accepted the amount of hassle the braces would bring and understood the benefits.
If your DS isn't happy about it, he will be really annoyed every time he has to have the wires and bands changed over, he might not commit to the extra cleaning regime needed so as not to damage teeth and as others have said, may not accept the ongoing maintenance required to make it worthwhile.
If he's happy and doesn't have issues with his confidence when smiling etc, leave him to it. If he doesn't qualify for NHS treatment it clearly isn't enough of an issue to cause problems.