If company A manages to convince Oracle to use CommonPaper's agreement, it clears the way for startup B to use the same agreement, without spending months on lawyers!
If both sides are arguing for their own custom template, then it's basically an arm wrestling match and whoever has the most leverage wins. If one side instead says "We adopted this independent standard created by attorneys from a bunch of companies" they get more leverage while being less adversarial.
Our early users saw a significant increase in the percentage of deals on their own paper (which is/was the standard) before they could be getting any benefit from the customer having seen the agreement before.