"You cannot study what -by definition- it's impossible to observe or measure directly or indirectly"

You're limiting knowledge to the hard sciences.

That kind of thinking is not scientific, but merely Scientism.

You're also ruling out many scientific domains, e.g. history which operates according to the historical method.

Theology (in the original Christian sense of the word) stands on the historical method. It's interested primarily in those historical events from which we can learn about God. If Jesus is not historical, if God has not acted in history, then there's nothing to know about God, and there's no such thing as Theology.

Scientific value != value. I view theology as a study of how humans characterize their relationship to that which is beyond logic: god, infinity, existence, whatever. To me, this study has individual and collective value even in modern times, despite the fact that it has no scientific value.