If you have an API, you should be load testing it. You should test it frequently and consistently.
With that out of the way, here’s why: API consumers are like your end users of a website or app. Yet unlike sites or apps, APIs don’t have front ends or usage paths to follow. Instead, assuming you’ve built the right capabilities into your API, everything comes down to performance.
So basic testing of your API is fine when you want to achieve “works on my machine”-level performance. But that isn’t enough for professional use.
Instead, you should be testing your API’s performance under load - seeing how it will perform under the stress of multiple consumers. In other words, your REST API shouldn’t spend any time resting at all.