The coordinator has to provide hundreds of inputs and outputs (equivalent to hundreds of normal bitcoin transactions) to deanonymize a single UTXO. In fact double that cost as the attacker must prepare the UTXOs in advance by making transactions.
I can produce a hundred outputs from a hundred separate transactions for less than $10 at current prices and fee rates. Add in a variety of sources, intermediate transactions, mixes, coinjoins, etc., along the way to obfuscate things, and you could still do this for a trivial amount of money. The coinjoin fees would be irrelevant since you can just hand them straight back to the blockchain analysis company since you are paying them for their services anyway. And in an ongoing attack, outputs from previous rounds can be recycled in to inputs in new rounds.
Furthermore, it's also detectable by looking at the remixes in the coinjoin.
Beyond the scope of the average user, and we can't trust you to tell your users since you are currently selling them out to a blockchain analysis company so you can serve institutional clients for your own profit.