Zero knowledge proofs do not need to be "small". What kind of ZKP use-case do imagine that cannot bother to send 1kb of additional data? What does any of this have to do with decentralization? Why is decentralization a goal? Do you really believe that most research into ZK cryptography is funded by blockchain?
Try and expand your sources of information, I have a feeling that you are in an internet bubble :(
See for yourself[2]. Much of the recent developments of practical ZKP stems from SNARK. In the last few years there has been an explosion of new papers and tools around this - lots of it driven by blockchain and in some cases directly funded by it.
[1] https://eprint.iacr.org/2013/279.pdf
[2] https://en.wikipedia.org/wiki/Zero-knowledge_proof#Zero-Know...
These new ZK proofs are much different than anything in the last decades, and can be used without a blockchain. But they also do fit elegantly within the context of blockchains, like having a ZKP verifier running on EVM instead of a single website like keybase.io, to further reduce points of centralization.