With your own server and Web framework, you do all the work in provisioning the machine, configuring services, installing dependencies, building deployment and integration pipelines and, worst of all, maintaining all that when updates are released / something breaks. It is also harder to scale.

A serverless solution that eliminates the Web framework (and thus the stack in which is being run) does most of that for you, at the expense of extra cost or infrastructure deployment complexity, but once it is done, scaling and maintenance are easier.