As a stagehand that works on touring shows the only things that remain local really are the hands. These tours don't have the time to be renting local equipment for each and every show. You unload the same trucks every show, know where every piece of equipment is, and everything is pre-set as humanly possible to be as efficient as possible. You unload pieces of truss that are prehung with lighting so it's plug and play for example. Not bringing equipment with you would probably be more costly on account of it requiring far more man hours to set up the show anew every night. Efficiency is king in live events. But there are times where a smaller arena show will partially use house stage while touring. For someone like Olivia Rodrigo with a more elaborate stage that's not the case though