Wrong. A reamer MUST be in alignment with the bore it creates. If it is not, you can expect bellmouth and taper. You will struggle with size and straightness. A floating holder is highly recommended. If you don't have access to one, DON'T GRIP THE REAMER DEEPLY IN THE CHUCK. Hold it by only about ¼" of the end length, so it can freely move about in the chuck jaws (it will seek center easily that way). That will provide the best possible scenario for the misaligned reamer. Mean time, get the tailstock aligned as best you can, to limit the error the reamer sees.
One more thing, and if you are already doing it, forgive me. I don't have enough time at my disposal to read the entire thread again, and I don't remember. Don't drill, then ream. The hole you create is likely to not be on location or straight unless you bore before reaming. Best scenario is to not ream at all, but bore to size.
In the post above you said the reamer quit cutting, although you fed it deeply. It didn't "quit cutting". It ran out of material to cut because you hit the back side of the wheel. The length of deposit in the flutes represents the depth of the part, and does NOT represent how deeply you fed the reamer.
H