I always carry Kairyu with me
'' share the same goal ''Alain wasn't a rival. Rivals are people who compete for the same goal, or who want to be better than each other.
Ash and Alain weren't competing, nor did they wanted to be better than each other. Before the league, for Ash, Alain was a random guy he battled twice. He didn't even know if he was going to see this random guy ever again.
Alain: Be the strongest person using Mega Evolution
Ash: Pokemon Master
Okay, it's not the same although it involves the same effort in battle, so who else shares the same goal as Ash? Gary before changing targets?
So Ash has no rivals.