It's not about protecting us but the sources.
All the major exchanges use blockchain analysis softwares mentioned earlier. So it won't really matter that you extend a chain of addresses of a coin that rely on a transparent blockchain, to hide the final use. It is absolutely not guaranteed to help.
Coinbase is generally used by newcomers only, not anymore by crypto enthusiasts after educated (except Coinbase Pro for some specific use). They became giants for the simplified access, by applying outrageous fees from a complex pricing structure, and are indeed known for being picky about surveillance, freezing and suspending accounts, filtering selectively both outward and inward transactions on occasions, which are not practices that gets much love from the community.
There are several other fiat to crypto exchange alternatives that are used by more advanced users preferably : Kraken (USA, didn't yet increase fees now that the cryptos lost their popularity), Bitstamp (Luxemburg with EU Bit-licence, increased fees, now almost as bad as Coinbase), Bittrex (NY, USD fiat only), Bitfinex (suited for large sums >10k), Bitpanda (Austria, for cards, perfect reliability), Wirex (UK, for cards, some issues), all just as heavily regulated, with the highest reputation, offering superior services.
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It can be made SO much simpler. About the exchange route alone (not the best)
Get the latest Monero price, XMR market cap, trading pairs, charts and data today from the world’s number one cryptocurrency price-tracking website
coinmarketcap.com
Sort by "Pair" and search for the exchanges that offer XMR/EUR and XMR/USD trading to figure out the current ones accepting fiat deposits. The highest trading "Volume (24hr)", over a couple days, is usually a good indicator that it's the best current choices to follow, just from user adoption. You can review the top 2/3 sites if you have time to waste.
At the moment, Kraken for the US and EU is unmatched, all things considered, but that can evolve (new competitors, evolving stricter regulation > removing pairs that happen with anom. coins time to time)
Acquire XMR at the exchange
Send your XMR to an external wallet (Monerujo on Android - you can buy an old new / used $30 phone for the purpose and/or reset your own to factory settings to be clear - or MyMonero on computer)
Preferably connect to the internet at a Cyber-Cafe or hotspot WiFi outside your home, if can't be arsed to protect your own computer via Tails and other tricks
Create sub-addresses within wallet, move coins to subs at least once or more (leads to varied inputs between initial exchange / end seller and you)
Pay the seller with XMR (request it), or BTC via the service XMR.to (directly integrated into Monerujo, or website - no need for Tor, if outside)
This will require zero unnecessary coin conversion (procedure hassle which everyone is complaining about) via unsecured external site that could betray you ...and will be much more economical to boot !
Just Kraken is between 3.5 to 30 times cheaper than Coinbase depending on configuration (plus considering hidden costs), then moving XMR is less expensive than moving BTC, less fees lost again between wallets and at another coin exchanger in between (tx/spread/slippage/trading fees bundle packaged - just like XMR.to, which by the way is not cheap and applies a few % in disguise)
Be straight forward, no need to complicate cryptos, save stress, time and money, between 5-12% in total (I was a trader for 12 years, including 4 on cryptos, registered on more than 50 sites, practiced, studied, tested on a daily basis)
Apply common sense (don't use your own computer if you have no energy or talent to secure it)
Pick the right exchange & deposit method (wire transfer instead of card)
Most importantly, think your coin/site selection in advance to navigate through less services/movements. The correct anonymous coins will improve the anonymity quest by default the most (opposed to internet privacy), in front of any side precautions you can think of and errors done because it's a complicated topic with many devilish details not to override (the number 1 rule of a Bitcoin guide for illegal use will always be to NOT use Bitcoin)
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For Bitcoin and cards, BitPanda will cost about 2.5% (1% for the deposit + 1.5% trading on the buy side) in total, Wirex slightly over 2% (1% + 1%), Coinbase +/- 4.5% (4% + 0.5%). Bitpanda offers withdrawal fees above a certain amount (cost of N, for sure)
For Monero/Bitcoin and wires, Kraken will cost less than 0.16% (cost alone of a limit order + spread partly won, fill almost guaranteed) or 0.26% (market order, guaranteed fill), while Coinbase 0.5% (more or less, from slippage / market conditions that are obscure less transparent than with Coinbase Pro trading, which is possible to use, being verified at Coinbase)
Note : if you use plenty of services/merchandisers, Bitstamp (for europeans / EUR wires only really, or others with card at 5%) offers 100% unlimited free withdrawals, then eventually it can become more advantageous than paying less trading and fundin fees (Kraken), otherwise it's usually 0.0005 BTC per withdrawal everywhere atm (a couple $ depending on BTC price, varying) - at the times the network become heavily congested and miners charge way higher fees (in the range $20-$40), it becomes even more beneficial