LOL... I'm sure that scientists the world over now rest assured knowing that they have your leave to define science in the traditional manner...
At the same time, it is only appropriate that such a definition be acknowledged for what it is (a subjective choice on the part of the observer) and that any further explananations and interpretations of data be understood with this choice in mind.
Anyone who looks at scientific data, and makes nonscientific conclusions therefrom (such as looking at a the fossil record and saying, "there is a God," or pointing to science and saying "this proves there is no God") is not doing science. And, yes, I agree, it should be understood that they are not doing anything that can be properly be described as science.
Why is it necessary to assume that an intelligent designer is beyond the pale of science? Is such a thing purely inconceivable? What if George Burns really did design the universe, and still maintains it? If it is an objective fact, then it is within the realm of science to seek it out, regardless of whatever religious implications might result.
Because science isn't the search for "objective fact" in the sense you mean. It is the search for natural explanations for the facts and phenomena of the natural world. And the reason for that limitation is that it works and it is effective; it has led to remarkable results and a wealth of knowledge and undeniable advancements.
And it isn't because of "religious implications" that this definitional limitation is defended. I mean, (if I may anthropomorphize for a second,) "science" is not attempting to monopolize the search for truth or insight or understanding, it's just defending it's good name. It is jealously defending itself from others who would call themselves science, without actually being science. If some knowledge or idea is going to be described as being "scientific," then it must meet the standards that the scientific method requires.
Here again you've place science under a restriction it is neither obligated nor empirically qualified to adopt. Science in general is "the observation, identification, description, experimental investigation, and theoretical explanation of phenomena." If it cares to restrict itself to so-called "natural phenomenon" it is free to do so, but I would expect it to state outright that it has thereby arbitrarily eliminated explanations that may be objectively true.