I suspect that the 4Kids delay might have lead to a more accurate dub when Funi did take over, though. If Funi had gotten the series first and the timing was similar to 4Kids, it would have premiered just as they were finishing off the Dragon Ball franchise. DB's dub had quite variable accuracy to the original, to the point of replacing all of DBZ and DBGT's music, and was a huge success. There are places where even DB's uncut dub has 4Kids-tier acting and writing and that's what those episodes are stuck with. Had Funi been handed One Piece, would they take the more accurate approach they'd already been leaning towards, or would they have tried to re-capture Dragon Ball's success?
I agree. Early Funimation tended to take quite a bit of liberties, especially with Dragon Ball. What many don't realize is that the way Funimation treated DBZ was very similar to how 4Kids dubbed many of their properties (replacing music, renaming characters and attacks, editing scripts, caricature voices) but it gets a pass due to nostalgia and because Funimation released episodes uncut. The worst part is we're stuck with it, and the closest they got to doing an accurate dub was Kai, but even then it was far from perfect.
Part of the reason I think Funimation's One Piece dub was successful was because they kind of had no other choice than to do it right after One Piece's reputation was extremely low thanks to 4Kids. It came a few years after Funimation found their footing with several widely-praised dubs (like Fullmetal Alchemist), so expectations were high. At the time nobody ever imagined the show getting a new license and a newer, accurate dub. If 4Kids never happened, though, I have no doubt that Funimation would have done pretty much whatever they really wanted with it, just like they did with the Dragon Ball franchise. They still had it in 'em at the time after all, since they treated Shin-Chan and Keroro (and later Dragon Ball Super) similarly.