I think you just didn’t get @0xbitcoiner‘s point: in the case of consolidation, all inputs are linked together, no matter if he sends them to a new address or not.

I would still use a new address since this slightly increases privacy: with a new address, it is not guaranteed that the output belongs to the same owner of the first address.

I must not be understanding something. What's the difference in terms of privacy in sending all utxo's to a new address or to address 1?