I agree with the idea of a foundation fabric for a base. This is one of those "form and function" things.
Your original question was about why you would cut on the bias. That question was answered.
Now if you want to know how to make this pattern for a purse. That is a different story. This is where function comes into play. Thickness and weight really aren't a problem in this case so sewing strips onto a foundation fabric can be your answer to solving your bias issues. I really am not sure you are going to save that much in fabric in the end (I didn't bother to plot this out and do the math).
Personally, I would go the foundation fabric route. Just my $0.04. (Prices are going up.)