Current situation of bilinear pairing protocols
That paper is misleading in several ways:

The DSA vs BB comparison: it is unfair because it compares DSA with the &quot;full&quot; BB scheme, which does not produce shorter signatures. The same BB paper describes a &quot;basic&quot; scheme that has a signature that is half the size of DSA. That's the whole point of short signature schemes (being shorter than ECDSA/DSA). This point is now moot, however, since a 2015 paper describing an attack that required pairing-based crypto to increase its parameter sizes, making short signatures not that short anymore (which does support the authors' claim, but that was not the justification they used).
They estimate that BB is 60 times slower than DSA but give no justification. While signature verification will indeed be slower, signing should be faster.
They raise the issue of the master key in PBC schemes. This is true, but only applies to ID-based crypto, and was known from the start.

Pairings are still relevant because some schemes can only be implemented efficiently using them. Zcash uses pairings to implement a zero-knowledge protocol; TPM chips use pairings to implement Direct Anonymous Attestation; for example.