Why are passenger required to put their phones in Airplane Mode during taxi to gate?
In general, they don't. U.S. airlines generally allow you to use your phones as soon as the plane lands.
Southwest:

Effective today, Southwest Customers with cell phones onboard may begin using them after the flight attendant gives permission to do so upon landing at the destination and taxi to the airport gate.

Source: Southwest Press Release from Sept 2, 2003
Delta:

Use of cellular devices prior to takeoff is not allowed per Delta policy so that flight attendants may properly prepare the cabin for departure and conduct safety demonstrations uninterrupted. Cellular devices may be used upon landing as instructed by the cabin crew.

Source: Everything You Need to Know About Using Devices on U.S. Airlines

Perhaps of interest, the rule against using cell phone during flight in the U.S. is not an FAA Federal Aviation Regulation. It is instead an FCC (Federal Communications Commission) regulation designed to prevent interference to the cell network as a result of thousands of phones flying around at 600 mph hitting hundreds of cell stations at once. In general, the FCC acknowledges that this rule is outdated and that this is no longer an issue for the current cell network. As such, the FCC has issued a proposal to remove this regulation. However, some airlines (including Delta and Southwest) have publicly stated that they will continue to not allow cell phone use for voice calls during flight even if it is legal, as the majority of their customers have indicated that they don't want to listen to their neighbors chatting on a cell phone for hours on end.

Delta will not allow cellular calls or internet-based voice communications onboard Delta or Delta Connection flights. Our customer research and direct feedback tell us that our frequent flyers believe voice calls in the cabin would be a disruption to the travel experience.
In fact, a clear majority of customers who responded to a 2012 survey said they felt the ability to make voice calls onboard would detract from – not enhance – their experience. Delta employees, particularly our in-flight crews, have told us definitively that they are not in favor of voice calls onboard.
-Delta CEO Richard Anderson