The ones who're unaware of privacy don't really care much about it but the ones who know its importance understand that it's very important thing. I believe someone with such high transaction history should at least know about privacy and instead of using a wallet with high transaction history he/she might prefer to use different wallets for different clients.
Using different wallets and different addresses for different purposes and for deals with different entities are very important. Bitcoin blockchain is not private so Bitcoin users must take care of their privacy by themselves, starting with wallets, addresses, change addresses, UTXOs, and also Tor when broadcasting transactions in deals with other entities, clients or trade partners.
Although, using of CEX will break connections but as we all know that to use a CEX one has to complete KYC first. When there's KYC then there's again no privacy but I guess at least a good CEX won't make life of such high rollers harder because it doesn't show any connections whatsoever.
There are centralized exchanges with KYC and there are other centralized exchanges without KYC but nowadays, there are less no KYC centralized exchanges to use.
If in practice, through Bitcoin blockchain, we made transactions to centralized exchanges where KYC is a mandate, we will lose our privacy to their exchanges, and it is one of many points for governments to track our money flows.