The reason they don't throw crossing routes to him frequently is very simple. Most teams don't play straight man coverage against the Rams. Therefore Austin is taken out of the game when he has to actually run a route that requires him to settle is a soft spot in the zone and become a stationary target.
Good thing they signed Welker then. He is one of the best zone-busters out there. He made a living finding the soft spot in the zone and burning teams time and again. Maybe he will teach Tavon the tricks of the trade.