I am not a Bitcoin dev nor have I any coding experience but I'd like to put this out there just in case this may be a viable solution to Bitcoin's on chain privacy. If there are any Bitcoin devs reading this, I'd love some input.
The basic idea is you have a pool of transactions you can pull UTXOs from to use in future transactions provided you show proof that a deposit to the pool was made first. There is no one that controls this pool, it's just a collection of transactions that have the same spending requirements. The oldest UTXOs are used before the newest ones. If the UTXO being used exceeds the amount for the eligible party to spend, the change is sent back to the pool. If the UTXO is too small, the UTXO of the transaction next in line is included in the input.
What it looks like in action: Alice sends a transaction to the pool. Alice sends Bob a key that only Bob can use that acts as a proof of Alice's transaction to the pool. Bob can then use that proof in order to use the UTXOs in the oldest transaction(s) to make his own transaction to the pool. Bob then sends a key to Carol to which she can do the same to spend to Nancy. This can be done ad infinitum until you leave the pool.
I can see this also working with second layer solutions. For example for Lightning Network, instead of Alice sending the proof of deposit to Bob they create a multisig sharing the proof. For Statechains the proof is turned into a statecoin. The proof basically takes the place of a regular transaction not tying it to any one UTXO.
crude sketch for visualization.
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