None of this, of course, addresses the original premise that the US should have built more of these reactors before engaging in any more oil-related conflicts. I mean, the US probably should not get involved in so many oil-related conflicts, but it is dubious for a number of reasons that earlier investment in these reactors would have negated the need.
At the moment, nuclear power plants produce energy for electrical applications, while oil produces energy for transportation applications. These are not interchangeable, so, no, building more reactors wouldn't have negated the need for oil.
There is a drive to move transportation to being powered by electrical energy, rather than oil (there's also a drive, funded by oil company profits, to delay or kill this shift), but it will still be quite a bit longer before that displaces a significant amount of oil use.
Oil is used for other things, of course, but while applications like heating can switch to electrical power, this also takes time.