Given enough time and resources, you'd be right, this would be sufficient. But remember the beginning of the movie - they explicitly stated that every year fewer crops could be harvested, which meant that most people had to work in food production, no matter what they did before. It was also stated that the population wouldn't accept spending going to interplanetary exploration instead of food production - they'd rather survive a little longer than to try and fulfill an impossible goal, or just to have a couple of people survive on ships/stations for a couple years longer, without any hope for long-term survival.

Under these circumstances (only a couple years left until starvation begins & no existing industry) it seems absolutely realistic that the government is able to throw together one hailmary in secret, without also being able to scale production up to save most people before they starve. Remember, the goal of the mission wasn't to measure the data they need to finish their equations, it was to send out one single ship that could continue human civilization on an inhabitable planet.

Had the future humans not intervened (by placing the black hole near inhabitable planets), humanity on earth would have died.