Kotlin makes an explicit difference between methods and properties. They are not considered the same thing; it just so happens that both are compiled down to methods in the end since the JVM doesn't natively support properties. As such, a method cannot implement a property since they're fundamentally different.
The reason why you can't implement a Java getter with a property is the same reason as why you can't implement a Kotlin-defined fun getX(): String with an override val x: String; they're just not compatible.
The confusion here seems to stem from how Kotlin allows you to access Java getters with a property-like syntax, i.e. val foo = obj.x is equivalent to val foo = obj.getX() if the class is defined in Java.
This is strictly a one-way relationship to make Kotlin code that interoperates with Java code slightly more compact and "Kotlin-like"; this syntactical shortcut doesn't extend to implementing the method as if it were a property.
Additionally, if you were to implement a method as a property, that would probably lead to strange effects. Arguably, it would be both a method and a property at the same time, which would not only be weird, but would likely lead to a lot of other unexpected behaviors and edge cases in the language. (For instance, how would it be treated when using reflection?)