The Algolia team struggled to find a suitable unit testing strategy for their React components until they discovered shallow rendering, a technique that allows testing React elements only one level deep. They found that this approach simplified unit testing but had limitations, such as not supporting simulation of clicks or access to component references. To overcome these limitations, the team developed an assertion library called `expect-jsx` which transforms passed React elements into JSX strings for better comparison. This solution has been adopted by other developers and is now widely used in the React community, with some libraries even incorporating it as a standard feature.