I’ve noticed this at the Bay Bridge between San Francisco and Oakland, but I’ve seen it at other bridges too. The towers aren’t right nexy to the bridge. I’d guess at maybe 30 t0 40 feet or more away, too far to be an advantege for crane work, but they do follow the route of the bridge from end to end.
I can’t think of any practical reason for doing this. 
I wonder if they’re going to move them when they finish our sexy new bridge?
BTW; I was going to call them telephone poles, but I know how that annoys power distribution people. 
Peace,
mangeorge
Because power lines already follow the roads at either end of the bridge? Because the geology of the riverbed has already been studied for planting bridge supports and that makes running them cheaper there? Because many cranes reach much further than 30 or 40 feet (we recently rented one that reaches 400 feet)? Because it’s easier to send inspectors driving along the bridge than motorboating elsewhere?
All just guesses. I’m not in the biz.
For what it’s worth, any major waterway crossing such as you describe is a costly endeavor for any utility. That’s why you see water mains bolted to many bridges. Another issue is easements. If another utility has an easement there, a utility can sometimes use that crossing for their own lines without purchasing another easement.
I’m over on the other side of the continent, so I don’t know about the Bay Bridge, but IIRC from my last trip (a long shot) the cables I saw running 20-30 out from the Bay and Golden Gate bridges looked more like supports for nets to catch jumpers than power cables. IIRC, the power cables ran immediately along the bridge at beloiw the roadbed level, and could only be seen from of the bridge. Of course that was only my interpretation of what I saw, colored by ill-remembered accounts of anti-suicide meaures, so I could be completely wrong.
If that is indeed what they are, it would explain the 30-foot distance. Was there specific evidence that they were power lines?