You might want to read again that she's entering a round for the first time.
What is your point? I acknowledge she is entering a round for the first time and testing this round with her non-private UTXO and her private UTXO.
The number of inputs make no difference. The fact is that if chain analysis company has de-anonymized Alice's coins and knows with certainty where all of her coins sit, which is trivial for the vast majority of people buying from KYC-ed exchanges, then no matter how many inputs she uses to coinjoin, the coordinator can attack her. Only if she uses a private coin, she can suspect of this attack (and yet, no certainty of her being attacked or her coins being deemed as "naughty" by the client).
Now it's time for you to argue that she should be running her own coordinator and join coins with herself before she enters another one. That would be the icing to the cake.
Why are you insisting that Alice can only have UTXOs that are known by chain analysis? Why can't Alice mine coins, use Lightning, or use Joinmarket to obtain a private UTXO?
Now it only takes Charlie, whose coins are also de-anonymized by blockchain analysis, and who will not engage in all this manual mumbo-jumbo. And after successfully attacking that user, it'd also give the impression to Alice that the coordinator is not malicious.
This means Alice and Charlie were in the same round, proving the coordinator is not Sybil attacking.