I won't enumerate these again as there's a lot of discussion about some of the possible new time controls on PerfectGent's original topic here:

http://www.chess.com/forum/view/general/discussion-of-different-time-limits-for-online-games

I'd support a few of these being added, particularly those that could provide more assurance as to the overall duration of a game while still maintaining sufficient flexibility on a move by move basis to play leisurely when desired.  I think that the most benefit of these would be realized in the improved pace of tournaments that employed them.

The major drawback is their inherent complexity compared with N days per move.

Yes, some more-so than others (hourglass clocks, for example, are quite straightforward).  I think the benefits, particularly to tournaments, outweigh the complexity and that once implemented they'll not seem so foreign.