Better Off Evil?
I have seen many fans comment over the years that they wish Jessie and James had stayed as evil and threatening as they are in "Pokémon Emergency!" At first glance, this appears to be a valid point; why not have Ash & company struggling against a duo who is truly villainous, good at being bad? Wouldn't that make for a better TV show, with stronger tension between good and evil?
Actually, it wouldn't. And here's why:
The Unexpected Trope of "Bad at Being Bad"
The truly villainous bad guy is a known and expected plot trope by now. What is unexpected is the "kinda-sorta-not-really-villainous" bad guy, simultaneously bad at being good and bad at being bad. This lends Pokémon much of its humor and charm, especially in the first two seasons. Who ever heard of bad guys who fail at being bad, right? This is hilarious! If Jessie and James had remained as sinister as they seem in their first appearance, there would have been so much less opportunity for exploring this unusual character trope.
(I do agree with critics of Team Rocket in that this trope gets quickly overplayed, especially during and after the Orange Islands season; it was actually one big reason I stopped watching the show, because my two favorite characters had been reduced to a flat joke and were not being expanded on or given chances for development anymore. But this problem is an example of bad character development practices--it doesn't mean that the character concepts themselves are bad.)
The Plot Balancing Act
Even as we laugh at Team Rocket's epic blastoff failures, we also see failures happening for Ash and his friends, which are not laughable at all. Just as Ash isn't much of a Pokémon trainer to begin with, Jessie and James aren't great spies or Pokémon thieves either--so the two groups of characters balance each other. This is so atypical for a "hero's journey" such as Ash is on; who ever heard of villains having to learn how to be bad, just as the hero is learning how to be good?
I believe this is because Jessie and James are both meant to teach us something about ourselves, just like Ash and his friends do. The most visible face of Team Rocket is a pair of villains who fail much more often than they succeed, despite what appears to be excellent planning--unlike Ash & company, the heroes who succeed more than they fail, largely due to being open to help from strangers (and just plain dumb luck, let's be honest). And yet, neither Jessie nor James gives up. They persevere and stay focused on their goal, adopting a "maybe next time" approach to catching Pikachu and getting back into Giovanni's good graces. As Ash & company teach us about being heroic and succeeding, Team Rocket, thus, teaches us about enduring multiple failures even when success seems impossibly out of reach--an important lesson for people of all ages to learn.
Team Rocket as Anti-Heroes (and Possibly Accidental Fan Favorites?)
For most of the first two seasons of Pokémon, Jessie and James' presence in the storyline is both comic relief and a second set of characters to be invested in. Indeed, the show at points seems to be as much about Team Rocket and their string of failures as it is about Ash, Misty, and Brock on their own journeys. That's why I think of Jessie and James as anti-heroes rather than true villains, especially as the series goes on; they begin as rather flat bad-guy characters, but quickly grow into characters who are much more complex.
Because of this, I get the feeling that Jessie and James were not originally intended to be quite the popular characters they became in fandom. Perhaps I'm mistaken in that--I've never read the manga--but at least in the English dubbed version of the anime, they begin as villains, but end up balancing the more juvenile-friendly heroic plotlines (especially Ash's) with a much-needed dose of adult-friendly humor and breaking the fourth wall. Thus, Team Rocket makes the show approachable for both children and parents/guardians watching, and later episodes of the Indigo League season capitalize on that, weaving in complex backstories and development for our suddenly-favorite "villains."