RE: Trading anonymously is hard, but not impossible. (See the Options!)
Myself? Hypothetically i'd do it like this...
Start with p2p markets if i want to convert my fiat money into BTC/ETH. It helps to be in a local crypto supporter's community. I am in a few here in Kuala Lumpur, Malaysia so it's just a matter of DMing someone "Hey you looking to sell?" (trust bothways is required of course, that is why i make sure it's one of my bros) and then it's just a matter of passing cash money to him during a coffee session or something like that.
Once i have the BTC, it's a matter of trading under the radar with non-KYC exchanges.
ETH is better since I can use Kyber or Bancor.
Of course, that is IF i want to trade anonymously.. I do have a few KYC exchanges for easy trades.. But for anonymity and privacy? Nothing beats p2p cash.
As you said, Trading anonymously is hard, but not impossible.