The O-rings and the temperature were only the last in the long chain of blunders, and that had little to nothing in common with reusability.
The construction of the SRBs wouldn't be much different with no reusability in mind. Indeed, SRBs of very similar design are to be used in SLS, and they are not intended to be reusable.
About the most important factor responsible for the disaster was misunderstanding of how the O-rings were meant to function.
The segments of SRBs were a consequence of the technological process; the boosters were manufacturer that way, regardless of the reusability needs. The segments would be connected with seals consisting of the O-rings, and ablative putty. The putty would act as a sealant keeping the pressure in, keeping the flames from escaping, and providing thermal isolation to the O-rings from the flames. The O-rings were to keep the putty from getting squeezed out by the extreme pressures of combustion. They were never meant to come into contact with flames and keep them from escaping, to any degree.
The putty appeared to be not efficient enough - all of it would burn away during the SRB burn. Then - the O-rings - not meant to withstand any flames - would still withstand them to such a degree, that less than half of them would burn through. And that fact - misunderstanding the fact that the putty burning through entirely was already a critical failure, and treating the degree of ablation of the O-rings as indicative of performance of the seal - allowed continued use of the faulty design.
The O-rings, not ever being meant to operate as flame blocker, not tested or prepared for such a role, would operate within specs for their designated task, and entirely out of specs for the task they were not meant to. It was pure dumb luck they would perform as flame blocker at all, and with changing weather conditions of course their behavior as flame blocker changed - nobody ever engineered them not to!
In fact - reusability - and in particular, recovery of the boosters - was a factor that could have prevented the disaster: the damage to the O-rings might pass unnoticed otherwise. Thanks to the boosters being recoverable, the damage was noticed, analyzed, and had the right conclusion been drawn, it would lead to redesign and fixing the error, e.g. replacing the putty with one that ablates slower.
Unfortunately - despite that - the problem was ignored, the damage accepted as "within norm".
So, in the end, the conclusion is pretty much opposite to the one you implied: Reusability is more likely to prevent disasters, than promote them; it allows to notice and analyze any problems that occur and would be missed in non-recoverable rockets until changing external conditions lead to a disaster. It just requires a thorough insight into the intended workings of the rocket, to be able to draw the correct conclusions from the observations. Without reusability we may lack the observations to draw conclusions from.