It's entirely reasonable blind speculation is my point. And assuming the three weeks thing was ever true and prominent, it likely isn't today. Why would they let all these series they plan to cancel run for six months if they knew right away? We're ALL just making incorrect points and massive assumptions here. I propose we ban all irrelevant discussion of Samurai 8 outside of "I did/didn't like this week's chapter" and why until we actually see some real indication of how it is received, which the TOC and random forums making up a tiny percentage of readers are likely not.
Iirc the three weeks is the earliest they decide whether to cancel the series or not. So I'm guessing it's usually a bit later for most series. However once they have the data of the polls for the third week, the 4th chapter would already be released and the 3 chapters after that are probably already finished as well with chapter 8 probably being done at that time. Then they usually have to give the mangaka time to end the manga, so let's say 2 weeks and you're already at the length of the shortest Shounen Jump manga in the last 5 years, Tokyo Wonder Boys.
Also, they most likely keep some series running even after they already decided to cancel them because they don't have enough series to replace them yet. I believe the current situation is a prime example for that. They ended Shokugeki no Souma and Hinomaruzumou in June and from then on, they only had 18 series instead of the usual 20 series in Jump. Now there is still one open slot available, yet there were only two new series last batch and they only filled one of the two slots while keeping most of the manga that weren't doing well.
This to me shows that they don't have enough new manga that they deem good enough to serialize. And while quite a lot of manga they end up serializing are bad and have no chance of surviving, I'm guessing the majority of manga they don't serialize is even worse. So it's pretty hard for them to find manga to serialize. So rather than axing the manga they already decided to axe straight away and getting a magazine that is half empty, they wait until they have enough new series to replace them with.
I think the reason why they currently have an open slot and decided to cancel one series instead of filling both open slots, is because they need to pay the mangaka of Saiyuki if they continue serializing his/her manga. Instead with an open slot, they can fill it with a lot of one shots to experiment (issue 33 to 39 all had a one shot) or special chapters to promote series from their other magazines. With lots of one shots, they can find out what readers want to potentially get more new manga they can serialize.
This is imo the most likely reason why they don't cancel new series straight away. Jump right now is in a situation where they need as many new hits as possible. Because if they were to cancel every new manga that hasn't gained an audience right now (except for the two newest ones because we can't tell yet) they would be left with 12 manga (already counting Chainsaw Man, because it seems to be popular). Even if you were to assume Samurai 8 has a big audience which I doubt, it would still be only 13 series.
Out of those 12 or 13 series, Neverland and BokuBen will most certainly end within the next year. I don't read Yuuna, but I think I heard somewhere that it might be ending soon as well. So basically, they have 12 series that are pretty much set in stone and at least two of those will end soon, which will leave them with only 10 series left. So they need good new series fast, but they don't have many new manga to serialize. So they have to keep the ones that will get cancelled running for longer because they don't want the magazine to be too empty.