All fully homomorphic encryptions (FHE) are converted into homomorphic commitments? The GSW one of the FHE scheme is widely used as a homomorphic commitment scheme to build lattice based ABE, homomorphic signatures and NIZK and so on. But I cannot find other FHE schemes to be considered as a commitment scheme such like that.
Is there a special reason why GSW is only one scheme regarded as a commitment scheme? or all known FHE schemes such as BGV are also commitment schemes?
Yes, all known FHE schemes are also commitment schemes (BGV included). The reason why GSW if much more often explicitly described as a commitment is that, unlike the alternatives, it leads to a commitment scheme with very nice property - for example, it gives a dual mode commitment (i.e. it can be perfectly binding or perfectly hiding depending on how exactly the parameters are generated), which is a very useful property (at the heart, to mention one application, of the constructions of fully homomorphic signatures).