They generally also break encapsulation (though you can kind of work around/sidestep this by making top-level visible errors more opaque)
Do you have a good reason you'd like to share for liking checked expressions? It seems like the reason you like it is because it's enforced by the compiler -- but I don't think this makes them the right choice, as the compiler could easily also enforce exhaustive handling of an Optional (or sum types like other languages).
If we limit ourselves to the case of Java 1.8, it is a fact that optionals are not checked by the compiler, so there is a solid benefit of using checked exceptions, solely that there is a compile time check of whether the exception was accounted for.
"...a good reason you'd like to share for liking checked expressions?"
Because they're the best solution for the problem. In Java.
The problem with Java's checked exceptions is misuse; turgid overwrought frameworks which obfuscate. Work closer to the metal. Eschew Spring, JPA, Annotations, aspects (AOP). All terrible ideas (making Java more dynamic) implemented terribly. (Quoting myself: Spring is an exception obfuscation framework.)
If you have to catch an exception you can't handle, revisit the design.
Your linked comment references sum types (Rust, Haskell) and multiple return types (Go). I haven't used those, so I can't comment.
The only solution better than checked try/catch/finally might be proper state machines. Experimenting with that is (far down) on my to do list. I'm also curious about Erlang/Elixir (and CSP in general), which uses a completely different strategy for error handling.
*"... Java 1.8, it is a fact that optionals are not checked by the compiler..."
Java's Optionals are a bad idea implemented badly.
The Correct Answer is using the Null Object pattern. Or just use LISP/Scheme. Also good ideas are intrinsic path expressions (vs method chaining) and pattern matching.
---
Top-thread, someone shared the "composition over inheritance" heuristic. This is more correct. Null Object and composition are like peas and carrots.
You mention "breaking encapsulation". So? Choose composition, make most objects dumb, implement the smart/active parts as yet another Interpreter. Problem solved.
I love checked expressions, hate Optionals.
I'll be happy when the language pimps stop trying to make Java look and act like a scripting language.
Edit: I apologize if I've offended anyone with my opinions. I hope this helps. http://bit.ly/1S1943H