I don't think it will become popular. AES-SIV has a main usage as key wrapping mechanism for its deterministic encryption properties. But keys are generally pretty small; parallel computation is certainly not required for minimal amounts of data.
With regards of performance: yes it can be parallelized. But on a modern machine you may need a lot of enhancements to beat AES in CTR mode + AES CMAC on a single thread that uses hardware acceleration. Intel's AES-NI + GCM acceleration can get throughput of 2 Gbps (that bits, mind you) on a single core of a Westmere chip (that's an old chip doing 2.4 GHz) - and that's within an actual IPSEC tunnel. You may want to go faster, but it might be that other components of your system cannot keep up. For server components that can have any amount of connections: if you have a 8 core chip (and 8 connections) you may easily saturate a 10 Gbps network card.
AES-PMAC still requires a single AES block encrypt per plaintext block. So even though it can be parallelized it will be outperformed by special MAC constructs such as GMAC or Poly1305 that do not require block cipher calls for each block of plaintext. You'd need at least another thread to make up for the difference in performance, and they you'd still need to manage the multi-threading.
I presume that the authentication tag is relatively secure, even if only the first x bytes are used for authentication tag. That's maybe nice for embedded platforms, but those commonly don't go for multi-threading / parallel computation. It's certainly an advantage over other MAC constructs that do not have this property, but not over others such as AES-SIV, AES-EAX or AES-CCM.
The one good reason why it may get popular is when the cryptographic community decides to switch from authenticated encryption to encryption that is largely impervious to nonce reuse (nonce misuse resistance).
But note that GMAC, as used in GCM mode, may actually performed in parallel as well; putting the parts together requires some additional calculations displayed here. So GCM-SIV may also be executed in parallel, using a less computationally expensive MAC calculation. GCM in SIV mode sidesteps the issues with the nonce that makes it extremely sensitive to nonce reuse. MAC calculations that use a block cipher are simply not that efficient.