Hmmm... Sure why not? A battle club has so many possibilities. The trainers we battle could always be around our highest Pokemon's level or the one in the team that we have when we go. At the most 10 trainers could be in there and they could refresh every 24 hours depending on when you registered-ex. register at noon, trainers refresh next day at noon. Or maybe you could go through rooms like the Battle Frontier.
Like Magmaruby and Aquasapphire said we could have tournaments which I'd be so stoked to see. Though I wonder how could the system work? Battle Royale-run around beating everyone and after your match there would be noticeably less people around until there's one person. A 1 vs. 1 standard tournament that goes weak to strong. A 2 v.s. 2 tag team match where your partners are people you've battled over the Wi-Fi connection or the NPC trainers like Cheryl, Buck, or Marley.