Why do we change the base year?
The change in base year keeps the dollar values meaningful to contemporary readers.  If we still used, say, 1900 as the base year for US GDP, the dollar values for today would be so tiny they would essentially be meaningless 'GDP units', which would make it harder for people to visualize what the numbers really mean.

Note that, when the base year changes, historical GDPs go up, not just going-forward GDPs.  So the 1900 US GDP, in 'constant' 2010 dollars, is about 10x as high as the NGDP for that year, to reflect inflation over the 20th century; but that number does a much better job of conveying to readers living in 2016 what conditions in the US in 1900 were really like than using 1900 dollars would.