If a Cohen marries a divorcee, and they have sons, these sons are Challallim. Do they stop being Cohanim forever? What becomes of the children of the Challallim? And if that is the case, are not the Cohanim all come from the tribe of Levi would they not still remain Levites?
A Chalal is a son of Levi but not a Cohen. Nothing can change that, forever. His son's are not Cohanim as well.