I can already do these things in Lightning code, so why should I use Flow Actions?
Flow Actions are intended primarily for non-developers. Things like notifications can be done without writing any code. If you have the skill to build a Flow Action, we encourage you to publish it and make it available for others to install!
Lightning components support CORS calls today as long as the target site is configured in CSP Trusted Sites. So if Flow is using Lightning component is there a use case or need to use Local Actions to make cross domain calls?
The benefit of using a local Flow Action for web service requests is mainly that you won't have to write any code yourself.
Since External Services can handle authentication as well is there much need to use Local Actions?
External Services are powerful but have a few limitations. For one thing, they go through the Salesforce Cloud and require a firewall entry point to access a company's on-premises servers. Local Flow Actions can be set up to make Direct Data Queries to on-premises servers. Also, External Services don't provide access to Browser features like page creation and toast display.
However, the authentication used by External Services is handy. You can create a Named Credential and use it to get access to a web service. We anticipate that may Flow Actions will also use Named Credentials to establish OAuth connectivity to web services.