As I remember it, the author says that Eisenhower was focused on strategic value of investments into space, and he felt that the US had a large lead in areas that mattered (ICBM technology) and chose not to invest in what might be considered vanity projects.
I believe he also claims that letting the Soviets be first to launch a satellite was intentional, since it allowed the Soviets to establish the precedent in international law that it was OK to send satellites over your neighbors, and if the US had been first the USSR might have protested.
https://www.nasa.gov/history/sputnik/begin.html
"Wernher von Braun showed me one of his mock-ups and told me of his plans for orbiting a satellite. He had been unable to obtain the authorizations and funds required to put an actual satellite in orbit; but according to his estimates, he could have done so many months before Russia's Sputnik I was launched-at a minute cost as measured by present-day space expenditures."
"Why was the Redstone-von Braun satellite project not supported? Answers vary with the person talked to: The Navy's brilliant developments in satellite instrumentation had tipped the choice to Vanguard, and budgetary restrictions had prevented a paralleling project. The name Redstone was too closely associated with military missiles. Vanguard offered lower costs, more growth potential, longer duration of orbiting. We would eventually gain more scientific information through Vanguard than through Redstone. To these observations, l can add from my own experience that inter-service rivalry exerted strong influence; also, that any conclusion drawn would be incomplete without taking into account the antagonism still existing toward von Braun and his co-workers because of their service on the German side of World War II."
It’s not that Korolev was irreplaceable necessarily, but the soviet union being what it was his death logistically derailed the space program.