Going in another country to preach makes more sense than going to build something. Those who go out on construction projects spend most of their time working on the project, not much in discussing the bible as missionaries would.
Another though that crossed my mind is the fact that everyone knows that they went out to do this sacrifice. If they simply provided a monetary donation that would have the exact same effect, no one would know. You won’t ever have someone taken as an example in a convention where a brother would explain how he gave away 30% of his salary. On the other hand, you have plenty of people going at the front boasting about all the blessings from going on construction sites in some poor country.