This answer is in response to the question in the title, “Shouldn’t Optional be Serializable?” The short answer is that the Java Lambda (JSR-335) expert group considered and rejected it. That note, and this one and this one indicate that the primary design goal for Optional is to be used as the return value of functions when a return value might be absent. The intent is that the caller immediately check the Optional and extract the actual value if it’s present. If the value is absent, the caller can substitute a default value, throw an exception, or apply some other policy. This is typically done by chaining fluent method calls off the end of a stream pipeline (or other methods) that return Optional values.
It was never intended for Optional to be used other ways, such as for optional method arguments or to be stored as a field in an object. And by extension, making Optional serializable would enable it to be stored persistently or transmitted across a network, both of which encourage uses far beyond its original design goal.
Usually there are better ways to organize the data than to store an Optional in a field. If a getter (such as the getValue method in the question) returns the actual Optional from the field, it forces every caller to implement some policy for dealing with an empty value. This will likely lead to inconsisent behavior across callers. It’s often better to have whatever code sets that field apply some policy at the time it’s set.
Sometimes people want to put Optional into collections, like List<Optional<X>> or Map<Key,Optional<Value>>. This too is usually a bad idea. It’s often better to replace these usages of Optional with Null-Object values (not actual null references), or simply to omit these entries from the collection entirely.