You certainly wouldn't want towers, but there's no need for towers across most of the bridge. There's just a narrow ship channel in the middle and the rest of the bay is shallow. Where it's marked as the tunnel, they could put a bridge just above the water level, supported by piers from underneath, just like the San Mateo Bridge.
I wonder if the SFO Airport would be friendly towards rebuilding the Airport BART station as a through running station, with the BART line continuing across the bridge or tunnel to the Castro Valley BART line.