(1) The economic growth figure that's usually reported is real GDP growth. This takes into account inflation, but does not take into account population growth.
Example. You seem to be puzzled by why economists and politicians fret when real GDP growth is, say, 0.2%. The reason is that if real GDP growth is 0.2% but population growth is 1%, then real GDP per capita (person) actually falls by 0.8% (approximately).
In the US for example, the annual population growth rate has averaged around 1% the past 30-40 years. So just to keep real GDP per capita constant, the US needs annual real GDP growth of 1%. Any lower and that indicates falling living standards.
0% GDP growth means living standards (measured by real GDP per capita) are falling by 1% per year, which is pretty terrible.
(2) Your other concern — regarding why we don't use other measures of living standards — is well-founded. Criticisms about GDP and GNP are as old as the concepts themselves. Every student to introductory macroeconomics is taught about the limitations of GDP as a measure of living standards.
One big and important reason is that GNP and GDP are the oldest, most well-established measures of living standards. Their development started in the 1930s (Great Depression) and was institutionalized by the UN and World Bank after the war. Every country has had regular GDP estimates for a very long time now.
Other measures are less well-established, not as well-developed, and have fewer resources devoted to their measurement. So although GDP is not a perfect measure, it is the most standard and accepted one we have right now, and so that's why we use it.
In 2008, a committee that included two Nobel laureates examined some alternatives to the standard GDP measure (PDF report). At the time I thought that some real change would come out of their report, but 8 years later it seems that nothing has changed. GDP is still the king of standard-of-living measures. Other measures remain mere supplements, albeit very useful ones.