@BlackSnow check the abstract here Mimblewimble CoinSwap proposal
I hope we see outputs being sent to the coinswap server by default because it gives a nice property that you can’t have an output owned for longer than ~1day that has a traceable owner (given that the coinswap service outputs a big enough transaction) meaning that every single one of your outputs that has been on the chain for more than a day has no clear history. The mixer comes with an assumption that at least one mix node is honest. If that’s true then nobody will know the links in the large coinswap transaction. But even if all collude, if the linkage isn’t made public, it protects against 99.99% of the users knowing the links. That’s also a big privacy improvement - though it might depend on your situation. And you don’t need to care if you send the output to the coinswap or not, it should be possible to use it in a transaction if you need to because the coinswap service knows how to filter out the spent outputs effectively.
And yes, it comes with some fee cost, but this should boost your as well as others privacy. Everyone pays a small fee to increase everyone else’s anonymity set. If everyone does this, users work together to help each other stay private through larger anonymity sets. The situation might change when we have full blocks, but that’s not something to worry about for the next couple of years 
You can know whether an output came from the coinswap service (you can’t tell which was its output) by checking whether the coinswap transaction contained that output. To obtain all the coinswap transactions, you simply send a coinswap to every daily mix and trace the transactions in the mempool that contains your coinswap. Now you know which outputs were produced by the coinswap service.
It’s not a perfect solution by any means, but as I argued here Mimblewimble CoinSwap proposal - #40 by oryhp , I think it might have the best properties of the mixers I’ve found (at least those that work on large anonymity sets).