The main goal of Card Sorting is to improve a website’s or an application’s Information Architecture, to help designing how the information is organized and labelled.
The sprint is a five-day process for answering critical business questions through design, prototyping, and testing ideas with customers. Developed at GV, it’s a “greatest hits” of business strategy, innovation, behavior science, design thinking, and more—packaged into a battle-tested process that any team can use.
Proof of concept in software development is a controversial topic. The person that came up with a software idea is usually convinced of its relevance. And stakeholders usually don't want to spend time on something that is not even going to be included in the final product.