Adam Smith would agree that the benefits of free enterprise are a consequence of the human desire to make life better for others?

No, it won't

Explanation:

Adam Smith arrive to the exact opposite conclusion. That acting out in a selfish way, people will achieve the common greater good. As it is not the benevolence of the butcher or the brewer, or the baker that we expect our dinner but their self-interest to acquire wealth and progress in life.

The claim for acting out in behalf of others is a socialims qualm not a capitalism proposal