OP, you are 100% correct. You should also mention other "centralized" services like Wallet providers. When you buy most of these hardware wallets, they ask your personal information and they store this information on their own internal database. (Just a few months ago, hackers got hold of millions of people's email addresses that bought a "Ledger" wallet and they started to target them with Phishing emails specifically targeted at them)   

People also re-use Bitcoin addresses and when they use their single Bitcoin address at a centralized service where they required a signup with personal information (KYC requirements at some online casinos) ..they expose their whole Bitcoin footprint to the person who can trace and link these services to your true identity.