Can't speak for the PNW, but there are a few bridges on the Illinois River that are handled remotely from dispatch centers, so it is done in some locations. The EJ&E bridge just below Lockport Lock is controlled from the EJ&E dispatch center, and the lift bridge at Beardstown, Illinois is controlled remotely by BNSF, most likely from Ft. Worth. Before UP acquired them, the C&NW attempted to automate the lift bridge at Pekin, Illinois. This went badly. The bridge was lowered on boats transiting the span, the dispatchers ignored calls to open, etc. The captains and pilots on the Illinois started calling the USCG Bridge Division in St. Louis every time there was a problem, and the C&NW was eventually told to operate the bridge manually again. It still is to this day. After manual operation was reinstated, the tenders were calling the boats as they went through, thanking the wheelhouse guys for getting their jobs back for them!
Other rail bridges on the Illinois are operated by the train crews using the bridge. Either there is a bungalow at track level on each side with bridge controls, or they have to climb to the control house. Bridges at Seneca and Ottawa are operated this way. The old CRI&P bridge at Joliet is manned 24/7, as is PP&U bridge at Peoria. EJ&E has just finished a new bridge just below Dresden Island Lock & Dam (the old bridge was the most frequently hit bridge anywhere in the US), and it may be operated remotely, but we don't know for sure.
Tom