So, take this with a grain of salt - someone linked me this github because they wanted my opinion on the idea of Explicit Versioning instead of SemVer, so I took a quick look.
One thing strikes me as awkward, but again, I'm not invested at all in this versioning system so this is just me playing devil's advocate.
The problem I'm seeing is that The Why Page specifically mentions Laravel 4.x as an example of why one would need something else than SemVer to version stuff. But this entire section contradicts the premise, for one simple reason:
Laravel didn't start using SemVer until version 6, so version 4 didn't have to follow the MAJOR.MINOR.PATCH system, so they were introducing changes that weren't backwards compatible in minor versions. This isn't because SemVer is wrong, it's because they simply weren't using SemVer at that time.
Version 6 and higher follow SemVer ( patch notes, first item ), while versions up to 5.8 followed their own "paradigm.major.minor" versioning ( 5.8 patch notes, first item ).
So what does this tell me? It tells me the "WHY" is wrong and the entire premise is flawed. To solidify the reason why anyone would want to move away from SemVer, you should find an example of where SemVer actually fails in its own protocols, and you haven't demonstrated this.
As a side-note, your "Disruptive" vs "Breaking" versions really don't add much, since a breaking backwards-incompatible change would, by definition, always be disruptive to the user.