No drawbacks at all. In fact, it's almost better to not use stain since this will make repairing and refinishing the door much easier if that time ever comes.

I hope you have a generous overhang like your inspiration photo does. If not, you'll be refinishing on a regular basis: like an antique boat owner.

Mine is inset almost exactly like the inspiration photo.

Our wood door has a similar overhang and it's surprising how much rain and snow gets on the door. We used Watco exterior oil. Seems to be holding up well but easy to get soiled.

if you know finishes well I would upgrade the finish to system 3 or a fine paints of Europe varnish its will be worth it. seal all sides tops and bottoms included. just know that with out stain you will need more maintenance. as the color from the stain helps with blocking uv damage.