I Know it is nearly a Mortal sin to disagree with Yooper on this forum. But I do disagree. 14 days in the fermenter is fine; bottle or keg at that point, if the beer is done, and it should be. Generally if you drink it before 5 or 6 weeks it is not going to taste as clean, crisp and rounded as it will at 6 to 10 weeks. Depending on the beer most assuredly, but I mean pale ales and IPAs. And I am not talking about off flavors that do not belong in the beer.
YMMV.
Heck, it's absolutely fine to disagree with me! This is a forum after all. If we all had the exact same opinion and experiences, it wouldn't be a forum. Plus, sometimes I'm just flat out wrong! (Not about this, though- ) But if you read what I wrote, and what you said- we actually seem to agree more than disagree.
It's true that sometimes beer that has aged a bit is "cleaner". That is usually because of yeast flocculation and perhaps some protein precipitation. If this happens at day 10, there would be no advantage to leaving the beer in the fermenter until day 30. That's my point- not that the beer won't be improved with a little bit of age in the bottle or keg, just that the widely repeated mantra of "keep your beer in the fermenter for a month at least or it won't be that good!" is a bit short-sighted.
I'm not sure I think of a yeasty beer as having that "homebrew" flavor. I've had the same experiences as Bernerbrau- going to a beer festival that had a homebrew booth. One or two of the beers were excellent- but most of them had a "homebrew" flavor. I didn't see any chill haze or yeast in suspension- it was more of a cooked extract-y flavor with a hint of sweetness. I'm thinking that is what the OP means by "homebrew" flavor, but as I mentioned, I've been known to be wrong!