I don't see it as a going slow approach.
From where we are now to the first interstellar missions in a century seems like a pretty hectic schedule to me. You must remember that it's already been 30+ years since our trips to the moon.
The first lunar and Mars bases can be built by NASA and used as a gateway by the private sector to expand on. This plan is sort of like how the government built the interstate system so that the private sector could use it to expand. The massive expansion of the economy due to it has paid for the initial cost of it many times over.