I don't know how much it actually matters or whether only the flightless ones -- *Pinguinus*, *Mancalla* and AFAIK none others, plus the plotopterid pelicans -- could be counted as possible competition in the first place.
It's not transportation why cold currents are -- apparently -- essential. The nutrients they bring are what matters. Close to the Pacific coast of SA the Humboldt Stream is teeming with life, whereas farther to the west there's nothing but blue desert. Equatorial waters don't support such ecosystems.
IMHO it's just the same thing as with penguins -- the cold currents from the north don't reach the equator either. (That's particularly extreme in the Atlantic where the Gulf Stream keeps all cold waters north of almost Newfoundland.) Were is the southernmost auk? In California? Where were the southernmost plotopterids?