Your process is too long so buying bitcoin directly would be the best option than buying XMR to BTC.
There are lots of Bitcoin mixers or tumblers you can try Wasabi it has a feature to mix them or use Chipmixer.
I agree with this statement.
The process that you follow OP is definitely tedious as you can skip some steps which are unnecessarily convenient. As what Bitmaxz had mentioned, purchasing BTC from your local exchange (though some require KYC documents) and using a mixer can easily acknowledge and follow the anonymity factor that you are hoping for. Another tip of advice, avoid putting your BTCs in an exchange if you plan on long-term HODLing. I suggest purchasing a hardware wallet to store your BTCs safely and securely.
No, we should have to keep/hold our coins in our controlled wallets, not from exchanges if we wanted security and anonymity.