I presume the 4 frets the are shown with are of different heights, s that they can match the height of the guitar frets?

On a Fender-style fitting, the 'teeth' are going to be very thin and the two end teeth even more prone to snapping off if caught than on a standard nut, so I'd definitely file down the excess height on the top of the nut as much as possible.

From the site pic, the fret doesn't appear to be very well seated, which would concern me. Especially as there are no tangs on the fret to hold it in place.

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I'd have gone for a stainless zero fret, as it's going to get more wear than a normal fret. I'd also have ordered a couple of replacement frets whilst they are still available. You never know how long the company will exist for. Though you can always swap back to a normal nut if you want (or need to).