The 'solid rocket boosters' being constructed in segments because they had to be transported by rail from Utah. They had to be constructed in that state as part of the deal to get the politicians to vote in the finances.
One of the bidders on the contract actually wanted to make a monolithic SRB, but that brings a new set of problems and limitations, especially at large sizes (you can look up the Aerojet 260" for some more info).
The shuttle SRBs were built in 7 segments, some of which were joined together at the factory. The multisegment design was based on the flight-proven Titan SRBs, which supposedly would help with R&D costs. However manufacturing constraints (if the SRB just used the Titan design and scaled it up, they'd need bigger hunks of metal than anyone was casting at the time) and design tweaks led to changes that degraded O-Ring performance and potentially kept both primary and secondary O-rings from being properly seated. There was really a whole confluence of things that went wrong, and a lot of missed opportunities to fix any one of the issues that led to O-ring failure.
Plenty of people still use segmented SRBs today, especially for their modularity. The (first version) of the SLS boosters are based on the shuttle design, with extra segments stuck added on.
The bigger issue here was the politics between Nasa and it's contractors. The contractors told them that the launch would be dangerous at the temperature, but they were ignored.
Do I understand correctly that you're saying that the O-ring would be necessary even if the SRBs were constructed as a single long tube, instead of segments that are assembled together?
If so, would you mind expanding on that? I was under the impression that the only reason the whole O-ring and caulking of the joints was necessary was the existence of the joints.
[1] https://science.ksc.nasa.gov/shuttle/technology/sts-newsref/...
Do you have a reference for this? Seems very intriguing to me. To me it seems the last thing you would want, under any circumstances would be to have hot gases coming out anywhere near the hydrogen tank and you'd make every effort to contain any overpressure until it exited beyond the hydrogen tank.
The following is a link to his book, but I actually heard a presentation from him.
https://www.amazon.com/Truth-Lies-Rings-Challenger-Disaster/...
Rockets are incredibly complex machines, you could use this sort of post hoc reasoning to find cause and blame for any anomaly by saying such a part could have been done differently. You couldn't ever use this reasoning to make design decisions that prevented accidents.
Blue Origin is planning to build their big rockets in Florida near the launch site.
The O-ring failed because it was a bad O-ring, and no one in positions that matters appreciated it was a bad O-ring. Politicizing it into a witch hunt to make congress look bad doesn't do anyone favors. It just feeds existing rage.
Contractor: "We don't want to launch, we're worried about how the cold will affect the O-ring"
NASA: "Do you have any data showing that the O-rings will fail at 50°F?"
Contractor: "No, but we don't have any data showing that they won't fail at 50°F"
NASA: "We launched when it was cold before and nothing went wrong" (The coldest launch before Challenger was successful, although both of the SRBs had badly charred O-rings)
Contractor: "Once, and there is circumstantial evidence that the O-rings had issues on that launch. (managers kicks engineers out of the room). We're not telling you not to launch."
That said, the hardness of the O-rings wasn't the only issue (at least, by itself it may not have caused the Challenger to explode). There was some putty around the O-rings that had problems. It was known to let water in, and the night before the launch it rained and was cold enough that the water that got in next to the O-rings could've frozen and kept them from maintaining their seal. There were primary and secondary O-rings, but the secondary O-rings didn't really give good redundancy.