Historically, the distinction between GDP and GNW goes back (at least) to Adam Smith. Before Smith, it was quite common to measure a country's economic power by its wealth. For example, this was very characteristic of the Mercantilistic school in the 17th century. Following the motto "you are what you have", mercantilists suggested that countries should try to accumulate as much wealth (for them: gold) as possible. This was to be achieved by a combination of an export oriented economy and political measures to limit imports such as tariffs. Selling goods abroad and keeping one's currency (again, gold) they hoped would result in having more money and thus being more wealthy. This idea is reasonable for the middleages where the difference between having and not having money can decide about which country is able to hire more mercenaries and has the potential to decide wars.
For more modern societies a country's wealth (read assets) becomes less important. Adam Smith was the first to realize that the "Wealth of Nations" is not so much about how much money they have but rather about how much economic welfare they can generate. This is measured in the number of goods and services produced in a given year, nowadays known as GDP.
From today's perspective, why do we use GDP rather than GNW:
- Actual production is much more important to determine a country's productivity than its wealth
- Accumulated wealth (GNP) measures past wealth while this years production of goods and services (GDP) is a good indicator of future wealth
- There is probably also some path dependency. Given that hardly anyone ever hears about GNP, I agree with you that (despite all arguments against it) GNP is slightly underrated.