The absurd need for logical proofs for God

[Fake Messiah]

And because these things display appearances of complexity, design, etc, this makes it more probable than not that the agent in question is intelligent,

It doesn't mean that if something is complex that it is inteligently designed.

What we usually consider to be cleverly designed machines is a combination of matter that doesn't belong to us in a way that is useful to a set of people, in other words, assigning design to something is actually a subjective issue

No, it is actually very objective. If we see in nature some "cleverly designed machine" like a clock, we know that it is man-made because 1st we know that humans make them, and 2nd it’s because nobody ever observed a clock giving birth to the baby clock, and nobody so far observed in nature fossils of “primitive” clocks upon which today’s clocks evolved. So that’s the main difference of how we know that biological beings evolved and machines were made by man.

it's not difficult to see that there is no intrinsic property of design that we can assign to objects around us.

It doesn’t mean that if there is no intelligent designer that there is no "designer" because nature, from rocks to animals and humans, is designed by natural processes. That’s why rocks/ cliffs look one way in the desert, and the other way under the sea—because they follow the pattern of natural processes that can even be predicted, like when people design alien planets for SF movies.