I may have misunderstood this aspect of the movie, but it seemed to me that the government was determined to convince the public that space exploration, and NASA, were excesses of the past to be avoided. The spacecraft they asked Cooper to pilot was a type of craft that crashed during his testing of the ship, prior to the public (and false) shutdown of space spending.

If this ship had the capability to repeatedly leave planets without the rockets shown in the beginning, would they have been able to reveal that to the public? The rockets could have been used for the launch from earth to avoid making that disclosure to the public.

Also, it seems like another possibility is that it was simply done to conserve fuel. Maybe the small spacecraft was capable of holding enough fuel for the 3-5 launches shown, but no more? If it wasn’t capable of holding additional fuel that might be needed for the mission, the extra rockets for an initial launch seem like a fair idea, even if they were very expensive.

I don't know anything about this, so I could be very wrong, but to me it seems like there are some plausible explanations.