The phrase necessary but not sufficient refers to something that you’ve got to have, but it isn’t enough. For example, being divisible by 2 is a necessary but not sufficient condition for being divisible by 6. Odd numbers are not divisible by 6, so being even is necessary. But evenness is not sufficient because, for example, 8 is an even number not divisible by 6.
Wrongly believing that nice theoretical properties are sufficient for a good model is known as a reification error. I don’t know of a name for wrongly believing theoretical properties are necessary. Believing theoretical criteria are sufficient when they’re not is a sophomoric error. Believing theoretical criteria are necessary when they’re not is a more subtle error.
Maybe it would be helpful to use a phrase like “beneficial but not sufficient” to indicate that some property increases our confidence in a model, though it may not be necessary.