Exceptions aren't an implementation detail. They're part of the API contract. Checked exceptions make this explicit, but people don't like that because error handling is hard and pretending that errors don't happen is easy.
fail fast, start from scratch. you can't handle a network error in your application, but you can basically kill everything that lost network access to your database and recreate it where database access is still possible. but you don't need to do that in your application, your infrastructure should handle these and thats why most checked exceptions in the java stdlib are basically stupid. 90% of the stuff reuses exceptions for ease of use but 90% of the stuff should be runtimeexception and 90% of them should split them up, between stuff that I COULD recover from and from stuff that I can't (i.e. SSLException should be split into validation of certificate exceptions and protocol violations!!! that mostly can't be handled without reconfiguring the JVM!!!! I mean there is a SSLProtocolException but it's basically useless since it reports a totally different thing..)