Question: I have a acquaintance who lives in the United States with a young daughter who will be starting Kindergarten next year.

However, her preschool feels she should be "held back", because among other things, she does not appear to be interested in writing her name.

I do not live in the United States, so perhaps I am in the wrong, but is this a scam?

It certainly sounds like a scam. Preschools are paid institutions, while Kindergarten is free (public school system). In my country, you do not need to "graduate" kindergarten to be accepted into 1st grade. Thus, holding someone back from kindergarten sounds ridiculous.

Even if she performs poorly, I don't see how this would harm her academic career.  

I do feel that delaying her education by a year will be detrimental.

I am advising this acquaintance that this sounds like a scam, but I could be in the wrong.

What is consensus on this?

Answer: 
I'd say in this case the preschool is offering advice and not necessarily perpetrating a scam, at least by a simple definition.

Preschool is optional in the USA. It can be free if you meet some wage requirements, or if you're part of a church, work, or academic program that offers it as incentive or grace. You can't fail per say, but part of their job is to evaluate growth and maturity.

In our district, the Kindergarten entry requirement is you must be at least 5 years old with a cut off birthday of something like September 1st. If you don't meet that you can take an early entrance exam which involves writing your name, following simple instructions, ability to walk single file from point A to point B, etc. I saw a kid fail in the lobby because he cried when it came time to separate from family. They're looking for a certain maturity level as well, and a preschool will have some idea of the expectations.

The USA, which is ranked something like 14th in the world for education, allows for districts like ours to have zero say in whether or not a child is held back in one of the K-12 levels. You can get straight F's and the parents can still advance their child. So even in official education levels the idea of being held back is more of a suggestion than anything.

Unless the preschool advisor also happens to own the institution, I'd say they probably have no real benefit from trying to scam you into staying longer. In your case, I would say that if they meet the age requirements, then enroll them in Kindergarten. Kinder is not a daycare. They have an actual curriculum and writing your name is a part of it.
Technically, no, you can't fail pre-school in the US. If you are of age and your parents want to enroll you, there's nothing a pre-school can do to prevent that. 

However, that does NOT mean that this is a scam. There are plenty of good reasons to hold a child back a year before they start kindergarten if you suspect they are not ready. Children who are born just before the cutoff and end up being on the extreme young end of the age range for their class are significantly more likely to get [diagnosed with ADHD](https://www.livescience.com/54007-birthdate-adhd-diagnosis.html). They are also less likely to do well in sports. 

If a parent has a good reason to believe that their child is not ready for Kindergarten, there's little harm and potentially much good to be had in holding the child back a year.

A personal anecdote. When my son was two, he was enrolled in a pre-school program for three year olds. The entire year, we kept hearing about how he was delayed. The next year, my wife was on maternity leave and so he stayed at home. The year after, he was in a class that was right for his age. The way his birthday lined up, he ended up being the oldest in the class. All that year, we heard about how advanced and smart he was.