Zero fret size?

[viento]

I almost finished a slotted headstock neck for my 12-string guitar that I´d like to have with a zero fret.
Should this first (zero) fret have the same hight as the others or would it be better to have it a tad higher?

[printer2]

Why go to the trouble of a zero fret if you make it higher?

[yellowesty]

FWIW, I build with a zero fret and use fretwire for the zero fret that is 0.004" taller than the fretwire that I use for the rest of the fretboard. This allows low action on the first few frets while preventing buzzing on open strings.

Zero fret builds seem to get no respect (maybe because, at one time, they were seen in lower quality guitars), but they do offer some advantages: the depth of the nut slots need never be an issue; string wrap at the nut end is always clean; the bridge is moved a bit toward the center of the soundboard, the ends of the nut are further from the fretting hand, and some people actually like the look.

[viento]

Thanks for both of your answers!
@ yellowesty: for your convincing arguments.