I like Pikachu and I have to say it's a pretty great mascot for the series. For starters Pikachu is incredibly unique purely from an aesthetic point of view. In the world of cartoon characters, there have been a lot of knock offs. Plenty of cartoon mice to confuse Mickey with and plenty of cartoon cats to confuse Garfield with, but I can't imagine anyone confusing Pikachu with something else. Even if people mightn't recognise Pikachu by name, the funny looking yellow thing is pretty synonymous with Pokemon at this point. Pikachu also makes for a good allegory for what pokemon are in general. Pikachu being a rodent like creature with the power to store electricity while pokemon in general tend to be animal like creatures that have various natural or elemental powers.
I'm not into the anime at all really, so any favouritism Pikachu receives in the show doesn't bother me too much. I did watch the show as a kid and I remember things like 'aim for the horn' and other such shenanigans, but even then, I always sort of viewed the anime as it's own little side universe. One thing that did effect the games which I'm not thrilled with is Pikachu's new cry. It's not so much that I hate the favouritism being showed to it, I just really liked the old cry and don't like the new one. The old cry sounded like the noise and electric rodent might make. The new one sounds like a Japanese woman repeating a noise twice. If your going to go down that route, then you may as well pull out the Sly Stallone soundboard for all the fighting type pokemon. When sending out Hitmonchan, how about he says "ey watcha mouth".
It's also worth noting that Pikachu doesn't really recieve any special treatment in the games. Well save for cos-play Pikachu, but that aside, Pikachu and Raichu have never been the strongest pokemon in game. Even with the Light Ball, Pikachu is still pretty useless given it's poor movepool. Being the mascot of the series, I'd have thought that maybe they'd do it a favour by making it the best Electric type, but that's thankfully never happened, and plenty of other great Electric types have been introduced in every subsequent generation. So while Pikachu might get the limelight in the anime and in merchandising, other pokemon get their spotlight in the games.