Sure, two points is better than one but what's special about two? I'd rather have a graph. We have computers so there's rarely a reason to compress the data so much.
We often have to compress the data down to a single decision or statistic: yes/no should I accept the job offer, how much money should I save before buying a house, or what's the probability that I'll die in the next 10 years.
I hate to quote XKCD, but it's like saying your favorite map projection is a globe (http://xkcd.com/977/). Yes, you've preserved all the data, but even with computers, your beloved graph will not make it all the way to the end.
Preserving all the data is the logical endpoint but that's not what I was suggesting. I'm just saying there's nothing special about keeping two points.
I'd rather not feed two points to my decision algorithm, whether it's machine learning or a human looking at the data. It makes more sense to make some attempt to preserve the shape of the graph unless you have strong reason to believe it's Gaussian, and even then the assumption should be checked.
