Bill Tindall, E.Tn.
I am familiar with a mill in central NY that only saws cherry and maple. Bought 2 truck loads of cherry from them when we were in business.
You would be hard pressed to find 18" cherry logs at a mill in NY. And if you did and they were clean they would sell them for many $ per bd ft for veneer logs.
It all depends on what the wood will be used for and where the trees grew. I would be delighted to have a load of 14" cherry logs that grew in a dense forest and have no interest in an 18" log that grew with ample sun and had bunches of healed scars where limbs had been.
You are spot on about the tree center. A mill will typically box out at least 4" from a cherry log. It typically shatters when it is dried.