I think it's the explicit lack of executive power that's the important part, not the lack of a direct popular vote. There doesn't seem to be much of a difference between say, the presidency of Finland (elected) and that of Estonia (appointed).

In fact, I'd say that Ireland's (directly elected) presidency has been one of the most notably successful, particularly in the post-1990 period when it's taken on more of a "cultural" rather than "political" focus.