Rebuttal towards Janet's statement.
You get the same amazing high when you beat a gym leader or finally beating the elite or pokemon champion to become the pokemon master and I think it's a bigger deal because it's an accomplishment to beat the game, competitive has no amazing long term accomplishments unlike beating the pokemon and story mode with it, because your honored afterward for actually beating the game and it gives you an amazing high
You do the same thing in story mode. If a gym leaders too tough to beat, you can go out and train your pokemon and spend plenty of time with them while you train them the best they could be, so that point works for either/or. Also for you Jigglypuff point, even if you got it to level 100 and raised it that best way possible, there's no way it'll be able to stand up a fully evolved Charizard whose max base stats will overall be higher then Jigglypuff. Every pokemon has a max and min base stat they can get, and fully evolved pokemon or huge pokemon generally have a higher base stat. You'd have to evolve Jigglypuff to Wigglytuff to even raise it's base stats, but even then Wigglytuff base stats are low, so if you wanna be the best competitive battler then you have to choose the appropriate pokemon to do so.
Your last reason, you technically get the title of pokemon master by beating the game, not other players around the world. Competing for the top spot is extremely hard to do, and most people don't have time for it and the ones who do completely occupy the top spot so no one can have it except those few. So getting the top spot is far fetched for most players anyway.
Again Competitive battling is only a secondary function of the games, you have to complete the entire story mode to unleash the full benefits of competitive battling, if you don't complete the primary task which is the story, then you'll never get to fully experience the secondary experience of competitive battling if you fail to play the story. So the story is more important for the fact that it gives you a great feeling when you beat the game plus the fact it gives you full benefits to competitive battling, while before it only gave some benefits. If people only played for competitive battling, then you'd see few people being used with at low levels. Since you need to collect badges to fully control pokemon at a certain level and you have to complete the game to be able to fully catch all the pokemon in that region, if you don't, then don't expect full benefits of competitive battling. Also most people play for the fun of it as well, not the competitive nature of it. This probably been proven with competitive battling games general doing poorer in the critic department then the main games with a story. I already listed one example in my statement.