If consultants are honest and do their job well, I doubt that the reader of an application could tell. I also have no issue with using consultants. People who are unsure of how to proceed with an application seek advice many places. Some seek it here, actually.
An honest consultant will work with a candidate to develop an application. Saying that they "write" the SOP is a bit incorrect if the ideas in it come from the candidate. This might be especially true for non native language speakers applying outside their own countries. But the honest consultant will work closely with the candidate, not just put their own ideas to paper.
But a dishonest consultant would be more likely to provide "boiler plate" information, not really related to the candidate. Those might be easier to detect, but only if a given committee saw previous applications that were similar.
But for a lot of candidates who get in to the ivy league, their own parents may be good consultants who do all of what you suggest. Of course, the recent news also suggests a few are willing to pay bribes as well.
I think that writing the SoP, if done properly, is fine. But if a "writing sample" is requested from the candidate, that person should be the one to write it. But even there, seeking advice on what to say and how to say it is probably pretty common.