It records vernacular.
And vernacular is how people understand each other. When you say, "Science has nothing to do with belief," then most people are going to interpret that according to the common-use meaning. If I say, "I believe I turned off the oven," I'm not expressing a faith-based conviction to the idea that I turned it off, I'm saying that based on my best recollection of the evidence, I did turn it off.
If you want to communicate in a way that people will understand, then I don't think you should going around using the word "belief" to mean this nonstandard, technical definition without qualifications or explanation. And I definitely don't think that you should assume that anyone who disagrees with statements made with that nonstandard definition is simply committed to rejecting reason and evidence, as opposed to the much more obvious and reasonable interpretation that they're simply interpreting the word in the standard, common use way.