Doesn't it make more sense that they wanted to represent all three starters and show off the three evolutionary stages of starter Pokemon? It also makes sense to have all three Pokemon be of different size weight and speed. It covers all grounds. The iconic Grass/Water/Fire starter trio as well as the first/second/third forms your starter will undergo.
Squirtle represents the water type starter line as well as the first stage of your starter.
Ivysaur represents the Grass type starter as well as the middle evolutionary stage a starter can have.
And Charizard represents the fire type starter and the final evolutionary form a starter will reach.
He said he wanted Blastoise originally along with Charizard. He changed his mind to show off the evolutionary lines. Ivysaur was the last choice and not really a big deal in the long run. That's the point. The elemental type thing is part of it, but the point was more he wasn't doing any of this to "pander to Gen 1 nostalgia" either. That was honestly just a big coincidence. When the most recognizable design happens to be a Gen 1 design, and the most recognizable Pokemon for Starters are Gen 1? You go with that. That said, the middle lines have always been the most unpopular because they weren't severely interesting designs and basically slightly different from the first form. It's the 1st and 3rd people care about. From what Sakurai talked about, we might've just got Blastoise and Charizard instead, but he evolved his idea in the long run to make it way better(not balance-wise, uniqueness-wise. The type weaknesses were not popular. Fatigue sucked too, but to a lesser degree and it didn't actually do anything to make one particular Pokemon worse than the rest).
Besides that, Greninja is the only Pokemon chosen because of the Gen specifically. While Lucario seems like an example, there's him also being severely pushed and already got good reception right away. And then there's the gameplay mechanic that the team worked with. It is possible he was chosen as a "ideal Gen 4 Pokemon" though. However, the rest weren't. Pikachu was the mascot. Jigglypuff was popular in Japan and easy to implement. Mewtwo was popular as hell and the most most popular Legendary at that point, and still is, making the inclusion easy(at least for Sakurai). I already explained why Pokemon Trainer was more about the mechanics being important, which what you said is also relevant to it too. Pichu was chosen because of an easy clone, and being Gen II was the latest during development, easiest to add(coincidentally was also the mascot for baby Pokemon). Being Gen II may have also influenced it, but I don't remember any articles on that, just the clone part and joke character part.
So despite the tons of Gen 1 Pokemon, they all had vast and unique reasons being added. Not a single one of them were simply because "Gen 1".