I can't find a clip of the studio recording but this is Ab Major.
I know what you mean with the no open notes comment. In the verse Robben plays a DbMaj9 chord. If you accidentally hit the high open E string (or low open E for that matter) when playing that chord it sounds horrendous.
My main experience with thinking of songs in key signatures is classical ... but there are simply too many to list. Chopin, Bach, Mozart, Schubert, Beethoven, you name it, all wrote in F minor/Ab major. Some of the bigger ones are Beethoven's Appassionata (Sonata 23 in F minor), Chopin's Fantasy Op 49 (F minor), Chopin's Polonaise No 6 Op 53 (Ab), Schubert's Sonata D557 (Ab), and Beethoven's Sonata No 31 (Ab).
These aren't exactly "songs" per se, but I'm sure a dedicated soul could translate them to guitar if desired.
Jazz is a much stronger option, since the open G is present in Abmaj7, the open A can be played off for dissonant purposes, and the open D for #11, etc. etc. F minor has that nice high E string to use for a great Fmin/maj7 sound, along with the rest of the usual jazz shadings with the other open strings.
All this presupposes you don't do a Carlos Alomar and use a one-off tuning for whatever song you're writing, modifying it as you need to to get the sound you want.