What about your heart?

[Sephiroth]

Yeah, no. Only the strongest hearts get Nobodies (that is why there is so little of them compared to Heartless), while the strongest of those become human-shaped Nobodies.

Kingdom Hearts is very vague with being accurate with terms like "strength" and many things in the story were already shown not to be like it was thought by fans. Especially Nobodies.

It is even said, Nobodies are born when a heart is swallowed by darkness. A heart. The empty body creates another personality to live without the heart and the missing heart is tried to be replaced. Every other thing would not make sense anyway because the fragments would be lost. There is a certain strength in any heart, like there is darkness in any heart, but lost fragments are no option and would make it impossible for the person to return. And many Heartless existing has many reasons like there are many ways for them to be created, naturally, artificially, et cetera. It would not make sense to banish the physical part into "nowhere". "Strength" is a very general word in the story and very easy to explain in Kingdom Hearts because everyone's strength has its own definition since there is the fairytale-like thought of everyone having a reason to fight, friends who make one stronger, et cetera. Sora even says his heart is defined by his friends. There is like no one in the whole story who has a "weak heart". Either their darkness is strong or their light. And for both types Nobodies can be created. When something is so general you really don't need to say it is necessary. It is like saying "If someone has a talent". Everyone has a talent, no matter what and this also depends on what is defined as talent.

EDIT: So to sum it up, going for what is said alone you would be right but what is important is what actually is in the story. It is also said in the glossary of 3D Nobodies have no hearts even though this is not exactly right and this is not changed even after you get to know. And there are many such things. Even talking about both body and mind fragment for the Nobody is something that is misleading because of the story and the real definition of mind, which would normally also make it, so the mind, part of a Heartless (even if they act instinctively), especially if you go for the first definition of Yen Sid who calls a Nobody, an empty vessel which creates a new personality while the Nobody still has memories of his original past. Heartless also have memories of their past and they should mainly be the mind part because all the heart fragment part is pretty much equal to terms like "ego", "consciousness", "soul"; "will"; et cetera. Spiritual. Not everything in Kingdom Hearts is said exactly like it is shown in the story, especially Kingdom Hearts itself, Heartless and Nobodies are complex and not every word follows exactly what it really is. And strength is also a formable word here, you see.