There's nothing wrong with using the starters as, well, starters.
I agree, actually. In fact, personally, I prefer that the starters be used if the character in question is getting his or her first Pokemon from the local professor. (From anywhere else, you have a wider range of options.) At that point, unless there's a very good reason for it, I would prefer it if the following cliches aren't used:
1. Character gets their last choice, rather than one they choose for strategic reasons (even if it's a second choice). No, waking up late is not a good excuse for that. The situation is a cliche.
2. A mix of starters from various regions because the author doesn't like the complete set associated with the region in question. For example, Elm gives out Cyndaquil, Totodile, and Chikorita. It's just the Pokemon he gets to distribute canonically, and the anime implies that those are the typical starters he hands out. He does not mix and match, so he would not be handing out Turtwig, Torchic, and Squirtle, even if you like those Pokemon more.
But I think what pokemon are included in fan fics is irellevant if the writing in other areas is good.
Depends on the Pokemon. Sometimes, the Pokemon starter ends up being a violation to canon in itself because of what it is. In fact, I've explained this pretty thoroughly in the original version of Lukespade's fic concerning having legendaries be starters and why that doesn't work.
Likewise, certain Pokemon imply a lack of creativity. For example, if a kid wakes up late and ends up getting a special Pokemon that isn't of the three starters, chances are, it's going to be Pikachu because the fic in question appears to be a copy of Ash's quest. Alternatively, it's going to be Eevee because everyone and their mother who does this kind of fic either gives the main character Pikachu or that thing. If it's the latter, then most likely, you're probably heading down the typical, cookie-cutter OT story, possibly with a Mary Sue. (I'm not saying the Pokemon would be what defines cookie-cutter OT stories. I'm saying that certain starters end up being red flags for lack of creativity because the authors who write these kinds of stories look at
other stories in the same genre and tend to follow the same kinds of plot, whether they know it or not.)
Additionally, it implies something about the character. For example, I've seen a lot of Riolu starters, and every trainer I've seen with one tends to be the tough-guy type, possibly with a strong sense of justice. Why? Because the author's trying to match the starter with the trainer, and they come up with the idea that Riolu -- which they may like a
lot because "Riolu is cool omg" -- is a tough-guy kind of Pokemon.
So, really, the starter Pokemon
does have some weight with the rest of the story because the starters unfortunately imply that certain things will be true. It's not the Pokemon itself, however, so much as the fact that the authors who use those kinds of Pokemon as starters in a fic tend to follow a predictable track. That's why people say you should avoid overused Pokemon: because most likely, you'll look like you're following those tracks (and
not because we've seen 19028202 Eevee starters).