Agreed. But obtaining such a token/proof would still be an additional barrier kids would have to actively bypass, so while I don't think that's the best implementation I don't think it's correct to say there's no value there.
My bigger concern would be who gets to issue these tokens. If it's limited to a particular government, then that doesn't work very well on a global internet. And making the internet not global (blocking adults from accessing foreign websites that don't adhere to your scheme) is kinda authoritarian IMO.
If we're going to do age verification and blocking of adult sites, it needs to be local to the user's device (and thus under the control of parents, not governments).
E.g. Instead of mandating sites verify users, we mandate internet-capable devices sold to kids have certain content restrictions, the same way we mandate you can't sell alcohol to kids. To make this more effective than existing content filtering, implement some kind of legally-enforced content-labeling standards websites have to follow to be whitelisted on these devices. This way the rights, freedoms, and privacy of adults using adult devices is unaffected.