Important clarification I forgot to make before the edit timer ran out: Private channels don't get gossiped, so large batch splices of private channels might still be private. I would imagine even a single public UTXO getting in the mix could compromise the privacy of the entire transaction though. 

shibe

bitcoin

Splicing

citizen21

I think the issue is that it's possible to track Lightning channels through gossip, because nodes share what UTXO is backing the channel. There are plans to change this alongside Taproot, so that Lightning channels are identical to Taproot single-sig spends, and figuring out a way to avoid sharing the on-chain UTXO with other nodes. But I'm not sure how the second thing will work. The reason you need to tell nodes that you actually have this liquidity to route payments is to prevent DoS attacks (imagine I tell everyone I have 0-fee channels with loads of liquidity, only for them to try to route payments through me and fail). It'd probably require something very complex like Zero Knowledge Proofs to do. 

But barring both Taproot implementation and some way to avoid gossiping on-chain UTXOs, it should be trivial for chainalysis to track splices. 
