Private blockchains are incentivized to adopt public blockchain architectures because public blockchains are most economically vetted.
Regarding private blockchains growing to public trustless blockchains, that is not a trivial problem. There are new blockchain models that are being promoted (e.g. IOTA, EOS, NEM) which have not being studied enough by consensus researchers.
I don't know of anyone who really applied traditional BFT networks into public blockchain architecture, however, until Tendermint.
For example, who spoke or wrote of BFT fault accountability/attribution, and how it pertains to proof-of-stake models, before Tendermint?
There was also the 2011 paper that lamented the lack of good open-source middleware for BFT algos. Tendermint solves that engineering problem as well.