I don't think this is how history works, and here's why.

I would consider the gospels less reliable sources if they contained zero supernatural elements.

The thing about the gospel texts is that they are religious texts, written by religious people, who inhabit a religious world in which the supernatural is normal. Among both Jews, and 1st century pagan inhabitants of the Roman empire, a view of reality in which supernatural causes and effects was part and parcel of the universe was simply default, and pervasive, you expect literature produced in that context to evidence that kind of thinking.

The gospels, by nature, are religious documents. They aren't recorded to be 'reliable history by 21st century standards', they are composed to be persuasive theologically-loaded biographical-type narratives by 1st century standards. If they didn't look like that, e.g. if they were stripped of supernatural elements, they would be suspect documents because we would ask, "Hey, why is there no supernaturalism in this text, in a world full of it?"

A historian approaching the gospel texts interrogates them firstly on their own terms - what sort of text is this, what does it purport to portray, what would it signify to its supposed audiences, how would they understand it, what does it tell us about the beliefs of its author(s). These are the questions that help us understand the beliefs and practices of early Christians.

It is this that makes them legitimate sources. Reliable is another question. That's when we ask questions like, why do they tell this story, are they reliable narrators, do they have the right access to be authentic witnesses, is it more likely that they are reporting things that happened, or that they are composing pious fictions.