This is mostly for practical reasons: AcousticBrainz needs a unique and stable identifier to attach its analyses to, and MusicBrainz (Recording) identifiers happen to fit the bill.
I think the @AcousticBrainz team intend to eventually allow analysis of non-MusicBrainz tagged audio eventually, using MessyBrainz to identify submissions (and hopefully eventually tie them back to MusicBrainz entities).
(I actually thought this was once of the questions answered in the AcousticBrainz FAQ, but it turns out it isn’t. Maybe it should be added… 
)