The main problem that I see with MBFC, aside from the simple fact that it’s a third party rather than ones own judgment (which is not infallible, but should still certainly be exercised, in both senses of the term) is that it appears to only measure factuality, which is just a tiny part of bias.
In spite of all of the noise about “fake news,” very little news is actually fake. The vast majority of bias resides not in the nominal facts of a story, but in which stories are run and how they’re reported - how those nominal facts are presented.
As an example, admittedly exaggerated for effect, compare:
Tom walked his dog Rex.
with
Rex the mangy cur was only barely restrained by Tom’s limp hold on his thin leash.
Both relay the same basic facts, and it’s likely that by MBFC’s standards, both would be rated the same for that reason alone. But it’s plain to see that the two are not even vaguely similar.