What does “denying admission to and ED acceptance” mean? Are you saying if a school rejects the applicant in the ED round it will hurt them with other schools? If so, that is false.
Or are you saying if the student is accepted in the ED round and declines the acceptance, there will be consequences? Based on the second sentence of your post, I think that’s it. The implications here are more nuanced, but this is not responsive to the OP (and there are many posts on this board about the implications of – and options for – declining an ED acceptance).
The OP’s question is, what harm is there in switching an application from ED consideration to RD consideration?
Others have noted, the student may be giving up on an admissions boost. For schools that care a lot about demonstrated interest (Tulane, American, etc.), it could be pretty consequential.