As specifically about the 707-320C here, one has to ask why the convertible/cargo model became the default, rather than the all passenger 707-320B. It wasn't like that initially, it changed over in the mid-60s, and I suspect quite a number of aircraft never operated as cargo. It wasn't as if there was no downside - the additional -320C weight of door and floor strengthening was such an issue for BOAC that when London-Moscow-Tokyo began that although they had a number of P&W 707C in hand by then, a good proportion configured for passengers, they needed to order two new 707-320B for the service, which were actually delivered a year after the first BOAC 747s. Some 707Cs were initially used as stand-ins on the service, but they might need to leave the freight behind, as the difference in capability was notable.
Someone at BOAC bought a 707C to add to their fleet from Saturn, the US supplemental, on it seems little more due diligence than "it's a 707C, innit ...". It was apparently a notably different aircraft for cockpit layout and similar, to the extent that differences course was needed for both pilots and FEs.
The US military did an evaluation in the mid 1960s and decided the 707C was their choice for long haul capacity, at a time of substantial Vietnam build-up, run by mainstream carriers. Several thus ordered and received quite significant fleets - Pan Am, Continental, Braniff, plus supplemental World Airways. Just after their delivery the DC8-63F became available and the military changed their mind at the contract renewal to these, now to be run by the pool of supplemental carriers, and apart from this overtaxing Douglas at Long Beach whose sales team committed to them all getting delivered together, the 707Cs the initial carriers had got were now a bit of an orphan on their shorter route structures - Pan Am were OK for what to do with them now, but Braniff and Continental were rather left high and dry, and after various long-haul route applications which didn't come off they became early secondhand stock sold to various operators.