That is not a problem. However, the problem is that all the inputs that you share with a coordinator will come from a single Tor identity, and a coordinator will learn that certain inputs belong to the same user. Inputs may not be connected to each other on the blockchain (publicly available information) but can be linked to each other during input consolidation (information unknown to the public).
I thought of the same, but then I saw this:
We didn't explain, because it's trivial. By architecture, the Wasabi coordinator cannot breach the privacy of its users. It does not mean the coordinator chooses to not collect data, but it means it couldn't collect even if it wanted to. The coordinator only knows of the UTXOs to take part in coinjoins - so does the public - and that's not a privacy leak.
Which makes me believe that Wasabi wallet, which is open source, works in a different way, making coordinators just single points that help the users gather. I haven't fully understood how it works, so I don't hold my breath about it. Perhaps, one more knowledgeable can give us a helping hand here.