This reminds me of an idea I may have only shared in chats before (I couldn’t find it on this Forum):
Let’s say your wallet has some received outputs that you consider tainted by the potential of the sender identifying you as their owner. So you might want to make some 1-input 1-output transaction with them and have it aggregated with other random transactions to reduce the taint (mixing).
But how to ensure aggregation? One way is to attach this wallet to a grin node and wait for a dandelion stem path to come across your node, at which point you could aggregate it with the transaction passing by. You can avoid adding your own kernel by proper adjustment of the offset. This is not safe in general, but appears safe if your excess is between your inputs and outputs exclusively.
You can either pay the likely increase in required fee yourself, or wait for a fee overpaying transaction to come by.
This scheme shows that paying a high fee is not only useful to get priority in case of full blocks, but also as an incentive to get aggregated with other transactions. Fees pay for priority and/or privacy.