First of all, we see the player character running to the bench. It is a goal. It is a destination. You might be thinking that it's normal, considering how you always walk towards stuff in real life, and in Pokémon games.
You'd be wrong. The character stares at it for a while before he sits. About a second, just staring at it. I'm sure that if the game was more detailed, we would see him breathe a sigh of relief and an expression of accomplishment will take over his face.
Then he sits. Go back to the video, and watch that part. He doesn't just sit on the bench; he acts exactly how you would act about meeting your bed after a long, tiring day at work or school. He doesn't just sit on the bench, he lets the bench consume him, and fall into it, because he appreciates the comfort of sitting.
And then what happens? The camera changes angles! Not only that, but it is slightly panned upwards! It reinstates the importance of sitting on benches. AND THEN IT LINGERS FOR ANOTHER SECOND OR SO! The camera knows how important the bench is, and how much it means to the player. And look at him! He's absorbing all the beauty of the world, like he's finally home!
I don't know about you, but I would always save inside a Pokémon Center, or right outside of it, because I want my character to rest. It's called empathy, caring, and being nice to others. If you don't like sitting on benches, or if you're not excited about it, then you're clearly an evil person, and I suggest you visit this website