I've been paying pretty much all bitcoin invoices that way for several years.
Blockchain sleuths would never be able to tell if a bitcoin transaction was just an exchange shuffling coins or if someone like me was actually on a different and opaque blockchain.
That depends on the nature of the investigation. Say they bust an illegal website and now have their subscriber records. If your bitcoin transactions match those of a subscriber to the website, they have more than enough info to come after you. With the website transaction records in one hand, and the public blockchain in the other, it would be trivial for an investigator to get a reasonable idea of who you are and where you live. Unless you spin up new accounts for each and every transaction, and mine your own coins, the public blockchain means they can identify patterns and make connections.
(I won't quibble on the technical definitions of reasonable suspicion. Suffice to say any such match will be enough to get a warrant and turn your life inside out.)
so secondly the bitcoin transaction would have been executed by someone else, from a mixer. The mixer was instructed by my transaction to it from an opaque blockchain, as explained earlier. Your rebuttal implies you have never seen the differentiating features of Monero. It is a public blockchain, but transactions are not linked.
Say they shut down an illegal website that subscribers paid 25$ for every month. If they see that your account paid out 25$/month, but stopped doing so when the website shut, then that's strong enough evidence for a warrant regardless of the exact path of transactions. That can be done via the blockchain far more easily than trying to gain access to bank records.
Will you just try using Monero before you say another word?
First, your assumption relies on having a nexus currency of Bitcoin to begin with, when Monero could easily be the base currency someone maintains a balance in. Monero has USD markets and has many default countermeasures towards linkability.
Second, your assumption relies on just not seeming to know how Monero works.
Third, I want to clarify that I'd be open to rebuttals if they actually acknowledged technology thats been around since 2014, but you are making rebuttals about rudimentary bitcoin mixers from 2012 when thats not even what we are talking about.