How you cut the link can also become problematic. It also doesn’t prevent you from future leaks that can be traced backwards. It’s extremely difficult even if you do everything right to maintain privacy on a public ledger.
Discussion
Currently, yeah, it's way harder than it should be, but that's still the right place to do it. We just need to keep building the tech. Privacy CAN be coordinated around Bitcoin and we should build the things that make it work well.