Hi Erik,
There are a strong arguments for and against pairing based sigs in Bitcoin. One very strong argument in favour over non-deterministic signatures like Schnorr over BLS is it enables a kind of signature encryption called "adaptor signatures". This construction is key to many exciting up and coming layer 2 protocols and isn't possible unless the signature scheme uses randomness.
self plug: I have a paper on this topic called "One-Time Verifiably Encrypted Signatures A.K.A Adaptor Signatures"
LL