The pokemon trainer does not have three random pokemon, he has practically the same pokemon as Ash in the show. Charizrd, squirtle, and bulbasaur is supposed to evolve soon so that makes Ivysaur. Piakchu is the mascot of pokemon. Mewtwo is the most popular legendary pokemon. Jigglypuff is one of the most liked and famous pokemon in japan and was popular in the series a while ago. Pichu i understand that he wont make it back in but he was the most awiated baby form in the second series. Lucario was in the 7th movie and was long thought to be a legendary pokemon. he is a beast and should get in.
Okay, the starters weren't based on Ash's starters. Ash's Bulbasaur will not evolve because he's basically not used anymore except for in special episodes (like that one Battle Frontier episode). Other than that, Bulbasaur will never be a major part of Ash's team again, so Ash never gets an Ivysaur.
A theory for how the Pokemon were chosen for PT: Charizard was chosen as the starter with the final form because he's the most popular final form out of the three Kanto starters. For whichever takes the first form spot, I'm guessing Squirtle was more popular than Bulbasaur, so Ivysaur takes the second stage spot.
Mewtwo being the most popular legendary is an opinion. Unless you can give a source to how they determined who's the most popular legendary, I'm not going to take that reason seriously; however, I believe Mewtwo will return as the playable legendary because he seems to make the most sense with his backstory and lots of other reasons I'm too lazy to explain.
I'll agree that Jigglypuff used to be very popular in Japan, but after the second generation Jigglypuff was not a recurring character in the anime. This could be due to declining popularity of Jigglypuff. Of course, Jigglypuff is still fairly popular, but not near the same level as when it first appeared in the anime.
Pichu, no matter how much I like him, is probably not returning. All his positive aspects were given to Pikachu, but Pikachu just can't pull of the cuteness Pichu had with the blue goggles. Sakurai did say he was trying to either get rid of or change clones. That's why I believe Pichu's out.
Lucario was in a movie almost 3 years ago. He was thought to be a legendary, but so was Blaziken and Tyranitar at one point before their games came out. Being thought as a legendary should not determine if a Pokemon gets in, and "he's a beast" is not good reasoning. Being in 1 out of 10 (11th coming out next year) should not warrant an appearance as playable. There is a lot of marketing with him, but there's a lot of marketing for Weavile, Mime Jr., and a lot more Pokemon. That's why I don't want to see marketing as a reason. (I know you didn't mention marketing, I'm just stating this before someone uses this as a reason).