Logging all API requests can be extremely important for security and compliance. A lot of intrusions can be detected or investigated later on based just on log analysis. Without those, it's like going blind into a deep forest.
API is the first point of entry into most web applications (by definition). Application security penetration tools (the same ones used both by whitehat and blackhat researchers) rely on communication with your APIs to find potential for abuse. So this maybemay be your best (and often the only, since everything else can be spoofed or hidden by the attacker) reliable visibility into such activity.
For this reason, logs should be stored in "read-only" form that cannot be purged by any intruder. Consider relying on Cloud provider native logging, which is designed with this purpose in mind.