I believe there is still construction on the southwestern loop that runs from west entrance road to the south entrance road. BUT, I just traveled in a few weeks ago coming back from Cody. There were a bunch of us, and two vehicles took the northern route from the east entrance road that goes through Hayden valley (valley of the nuts is what I call it...thousands of morons and a hundred Bison) and over to the west entrance.
Two vehicles took the southern route. Those who took the southern route beat us to the west exit by almost 20 minutes. The delay was minimal, even though they say UP TO 30 minutes.
Here's a site to keep updated on the roads in Yellowstone...
Road Construction and Delays - Yellowstone National Park (U.S. National Park Service)
I don't believe I will ever go through Hayden valley again preferring the construction backups vs. the selfie crowd.