It is more than about using cookies, despite the regulations being informally called cookie laws, any tracking and storage of PII is covered.
> Would there exist any other method of implementing it that would be substantially different?
A checkbox or button, anywhere on the page, that you can click to opt-in or ignore to not op-in. Once clicked the site/app has consent to track that consent, so the box can stay ticked (or be moved out of the way entirely as long as a way to retract consent is easily available, perhaps via an obvious link in page footers). Done. Informed consent implemented in a way that doesn't irritate any user (those that care either way, and those that don't care at all).
They could even include a short bit of text begging people to opt in because it helps their site/app make more money from advertisers, without going as far as a pop-over or otherwise wasting a large portion of screen space.
> Its hard to imagine.
For those with very little imagination, perhaps.
> … ideal situation is that people … set … a browser preference …. Oh wait they already can.
Only with regard to cookies, and perhaps other local storage, which as I stated at the top is not at all the whole matter. And even within those limitations those options are rather ineffective against the experienced stalkers that the advertising industry consists of, because they can and will simply ignore things like DNT and will work around cookie/localstorage/other blocks using various other fingerprinting tricks.