Upon first glance, the Team Rocket trio look kind of stupid following Ash and Pikachu for so long. Like, he's one kid with a Pikachu. Nothing special. And there are plenty of other strong trainers/their Pokemon to go after. Giovanni doesn't seem like he cares much about Ash's Pikachu, let alone his other Pokemon, so the whole quest seems moot.

Except it kind of paid off. Ash is now the world champion, and Pikachu is the God of Pikachus. If Team Rocket manages to catch Pikachu now, they'll be legends within Team Rocket. Giovanni might even give them a promotion. I doubt this was planned, but even so, Team Rocket's single-minded pursuit of Ash's Pikachu kind of paid off.