Azure API Management offers additional capabilities out of the box primarily for rate limiting, security and caching.
As long as you've met the security requirements for your API in your code in Azure Functions then the risk is simply your API being overused or attacked. APIM's rate limiting capability would stop the traffic from reaching your API. The other consequence of Azure Functions receiving too much traffic is that on the consumption plan your bill will be directly affected.
API Management does generally feature in reference architectures when exposing API's for the reasons mentioned.
https://learn.microsoft.com/en-us/azure/api-management/api-management-features