The default options for monitoring Azure Web Apps can be useful, but it's only the beginning of the Web App monitoring options. If you want a really powerful tool for monitoring and alerting with dashboards and analytics, Application Insights is the tool you want to use. Application Insights can be created and linked to a Web App while creating the Web App or later.
Also, you can use a single Application Insight to monitor multiple Azure Web Apps. It's interesting that Application Insights is not limited to Azure Web Apps, but can be used with an application hosted anywhere, including other cloud providers or an on-premises data center.
