You can avoid that by chaining multiple transactions (each with a "normal" mix factor such as 4) with appropriately selected time delays. After doing this you can even destroy the private keys for the intermediate outputs, a form of perfect forward secrecy. Obviously this adds time, so may not be suitable for all use cases, but is another option, and is probably the most secure method overall.
Its even cheaper that way right? Because, say you are using mixin 3 and you do it 6 times, than you get 6^3 partners (216) but only 6*3 (18) in signature size rather than a signature size of 218 that you would get if you just used 1 transaction with a mixin of 218 instead. Am i thinking about this right?
Arguably. It depends how you characterize the anonymity set. You are paying an added cost for your own output-input pairs on each step relative to the number of truly foreign signers included, but from a third party tracing perspective it is similar to 3^6.
A function like that is reasonable. One interpretation of ring signatures is to be able to mix your own coins without relying on a third party mixer or mixing coordinator, so various different ways of doing that mixing in a wallet (= client in monero-speak) are possible.
ok so than another question. why do we technically need to wait for 6 blocks to do this process 6 times? cant you in theory set up the protocol in such a way for outputs from other transactions in the same block to be valid inputs to a transaction in that same block? of course if you were the only person who did this than it would give you away right away, but if everyone was doing it all the time, well maybe it could work. If it did work it would be effectively non linear signatures.
honestly i suspect it doesn't, it would limit the total number of available participants to the other people in that block rather than all participants in the networks history. less than ideal. additionally you would need to coordinate off blockchain with other people. but hey maybe its an interesting conversation. ive always been firmly of the opinion that bad ideas are still worth talking about so long as they are sufficiently interesting.