It would increase the United States’ power by creating a bond with Russia.
ex
The US saw Russia as it was in it's current state, and "empire". Russia during that time was one of the strongest countries (though ranked behind Britain and France), and an alliance with them would prove valuable. Not only was buying Seward's Folly a good idea through diplomacy, but also land space, and later on as figured out, natural resources such as coal, gold, oil, etc.