I rather like this. A represents major changes like a substantial redesign of the whole API, while B catches all other breaking changes. Tiny changes to the public API of a library may not be strictly backwards compatible, even if they don't affect most users of the package or require substantial work to address.
A problem with Semver is that a jump from 101.1.2 to 102.0.0 might be a trivial upgrade, and then the jump to 103.0.0 requires rewriting half your code. With two major version numbers, that would be 1.101.1.2 to 1.102.0.0 to 2.0.0.0. That makes the difference immediately clear, and lets library authors push a 1.103.0.0 release if they really need to.
In practice, with Semver, changes like this get reflected in the package name instead of the version number. (Like maybe you go from data-frames 101.1.2 to data-frames-2 1.0.0.) But there's no consistent convention for how this works, and it always felt awkward to me, especially if the intention is that everyone migrates to the new version of the API eventually.
