A long time ago, back in 2005, I rolled into this forum with a vanity post about intelligent design, making the point (in part) that ID is not the foil of evolutionary theory but of philosophical Naturalism.
Philosophical Naturalism, or the belief that all that we see must be explained only in terms of processes arising from within the system, is not scientific proposition as it is not testable. Rather it is a belief asserted about the first causes of things and it is further one that has developed very dogmatic consensus.
One of the effects of the need to bring about more belief in philosophical Naturalism is found in how the form of “evolution” that is frequently taught in public education is often hopelessly out of date with respect to the actual state of theory ... causing me to joke back in the day that it seems as if bad high school textbooks should be cheaper that good if they want to justify teaching out of date ideas as if biological laws of nature. What this is all about, rather, is that there is a need to teach ways of thinking about life that need no God, that needs no creator. This serves a socially transformative purpose rather than a “scientific” one which is precisely why bad textbooks don’t matter, they ultimately aren’t teaching evolutionary science but are teaching believing in evolution as a doctrine.
Intelligent design is NOT creationism, at least not in any Christian sense. It accepts all the notions bandied about by the evolutionists but is based on observations, often arising from the science of cosmology, that the universe is too perfectly balanced to not be inexplicable, as well as from issues arising from biological chemistry. ID as a philosophical matter was first proposed to liberate the science from the demands of the strict philosophical Naturalism.
ID was picked up by others who had what I’d term “other reasons to believe” than anything arising from science. No different than the secularist have latched onto evolution (and now man made climate change) as a way to advance their other dogs in the hunt.
That is why I, with backgrounds in both biology and theology, have never been more than passingly interested in ID (just as I am not particularly interested in Evolution).
Some people devote themselves to denying a distinction between your "philosophical naturalism" and the basic scientific assumption of "methodological naturalism".
But the enterprise of natural science does not itself deny the existence or influence of God, only posits that science cannot study such matters.
Natural science happily leaves the inquiry to other disciplines, especially theology and philosophy.
The natural science of our Founding Fathers and the Age of Enlightenment was built on the assumption of virtuous inquiry into nature as "the mind of God".
Only generations later did some people begin pretending there was no "Mind" to discover, just... well... random, nothing.