Hey, so, I just ended up finding this thread and it's definitely something worth discussing. Sorry for a post mortem revival about... post mortem.
Anyway, I always believed it was a lot of things. I was part of the fandom at the time so I saw all of it play out. Yeah, Funimation acquired the license while the 4Kids dub was still airing—even though the dub was confirmed cancelled in December 2006, there were still lots of episodes left to air in the US, especially since Toonami UK finished airing them long before. I remember that the Funimation dub was originally scheduled to begin in summer 2007, but Toonami kept doing so many Naruto marathons that it pushed it back to fall lol.
Anyway, because of the 4Kids backlog of episodes there was a seamless transition that had the Funimation dub picking up right where the 4Kids dub left off the following week... and yeah the Funimation dub only lasted about 6 months before it was removed. It was particularly odd, especially given that Cartoon Network's interest in keeping the show going is what led to the license being picked up so quick. From what I remember, the suits at Cartoon Network were changing stuff up in late 2007/early 2008, and it appeared they wanted to distance themselves from anime and focus on their original programming... which is why lots of live action bullshit came out of nowhere at this exact time too.
If you think about it, One Piece getting dropped isn't even the weirdest thing. Remember how I said Toonami aired all sorts of Naruto marathons? They aired the shit out of Naruto since it was a ratings hit and didn't even finish airing it... if I remembered correctly, they dropped it with about 10-15 episodes remaining until it was finished. That's why shortly after that, competitors Disney XD and Nicktoons began airing Naruto Shippuden and Dragon Ball Kai respectively. Then Toonami got the boot along with Naruto, along with all of the other anime that was on the block. It was clear that the new heads of Cartoon Network weren't interested in anime unless it was one big merchandise commercial for kids like Pokemon.
Adult Swim doing its April Fools Toonami airing in 2012 showed that there was still a market for anime on TV, especially since four years later, the anime industry grew a LOT thanks to the internet and streaming.
As for One Piece's reception at the time... well, its reputation wasn't great, but it was doing good enough that the heads at CN wanted to keep airing it on Toonami. So I guess it was doing good enough for the network. When the 4Kids dub was airing, One Piece's reputation was shit. Most had exposure to the 4Kids dub and nobody really had anything positive to say about it. Funimation immediately picking up where the 4Kids dub left off didn't do much to fix it either. It would take YEARS for this show to become successful, mostly thanks to the passage of time.
tldr; One Piece (both 4Kids and Funimation dubs) did fine ratings-wise on Toonami, even though most kids only sat through it waiting for Naruto to air. Cartoon Network lost interest in airing anime in the late 2000s and realized a few years later that it was worth airing again only after it became mainstream.