Does private tokenization fragment RWA liquidity?

RWA maxis pitch tokenized assets as a way to bring more liquidity onchain. But while tokenization brings TradFi liquidity, it could also isolate that liquidity from the rest of DeFi.

Some institutions use private chains or permissioned markets to meet privacy and compliance requirements. If an asset is on a private network, it may need some interoperability solution to access public DeFi markets. This solves for RWA privacy but fragments DeFi liquidity across different environments.

I'll give you one more example. Shielded balances also address the privacy bottleneck, but they create another problem. Say you want to use an RWA asset as collateral. If your position details are private, how does a lending protocol verify the collateral, calculate borrowing limits, or trigger liquidations when necessary?

What are your thoughts? How can RWA projects give institutions the privacy they need without fragmenting liquidity or giving up on DeFi composability?