One little historical point to begin with: Descartes didn't actually appeal to the Argument from Design at all. But you're certainly right that it has a long and venerable history behind it. It's the fifth of St Thomas Aquinas's 'Five Ways' of proving the existence of God; and, in some form or other, it goes a long way still further back than that.
Regarding the recent controversies (and perhaps explaining the 'oddness' of the trial), there are two issues that need to be distinguished. (i) Is it a good argument? (ii) Is it a scientific argument? The two questions are independent: both scientific debates and debates of other kinds (philosophical, theological, etc.) do get their fair share of both good arguments and bad arguments. We hope that, whatever the debate, the good arguments will win the day: but the bad ones deserve to be given a fair hearing too, so that what is bad about them might be exposed. Now, the recent controversies have centred around the question of whether or not ID is a scientific theory. If it is a scientific theory, then it would seem to merit some discussion within science classes in public schools: counterposed against alternative theories, perhaps, to facilitate a free and fair debate wherein the superior theory (whichever that might be) might vanquish the inferior. If it's not a scientific theory, then, whatever merits it may or may not have, science classes are simply not the place for it to be discussed.
I didn't follow the Dover trial in any great detail, but it did have strong echoes of an Arkansas trial in 1981, on an almost identical issue: whether 'Creation Science' (as it was then being called) should be taught in science classes in public schools. And, at that trial, philosophers actually were invited to testify. But these were not philosophers of religion, and they were not (as far as I know) asked to comment on whether they felt that the underlying argument was a good argument or a bad one. Rather, they were philosophers of science, and they were asked to comment on whether they felt that it qualified as a scientific argument at all, irrespective of whether it had any intrinsic merit. The witnesses maintained that it failed to live up to the criteria that define genuine scientific research -- it wasn't seeking universal laws of nature, it wasn't yielding explanations of known phenomena or predictions of unknown ones, it wasn't empirically testable, and its practitioners were overly dogmatic -- and the court agreed. As I understand it, this was also the question that the Dover court was asked to decide: not whether ID was a good theory, but whether it was a scientific theory. But the interesting thing about that 1981 trial (and, for all I know, maybe the Dover trial too) was that it launched a debate within the philosophy of science community. The trouble with philosophers of science is that they are decidedly prone to disagreements about what science is, let alone how its practitioners ought to operate. Some philosophers pointed out that many of the most central, paradigmatic cases that everyone would unhesitatingly regard as genuinely scientific theories would nevertheless fall short of the excessively rigid criteria for scientific status just listed above. There is no clear philosophical consensus about what makes a theory qualify as 'scientific'. Consequently, there is no clear philosophical consensus about whether or not the Argument from Design is a scientific argument.
Where philosophers are, I think, closer to consensus (although I'm sure there will still be dissenters here too) is on the question of whether or not the Argument from Design is a good argument. David Hume, in his Dialogues concerning Natural Religion (written in the 1750s, published 1779), argued that it was not; and his objections to it (which I'd invite you to follow up in detail, if you're interested in this sort of thing) are really rather powerful, and regarded as decisive by many philosophers nowadays. Hume showed (or purported to show) that little or nothing of religious doctrine can be rationally justified, through any arguments based on empirical evidence (or by a priori arguments either for that matter). Indeed, he argued that, if anything, the evidence would seem to tell directly against such doctrines. Admittedly, even outside this domain, Hume didn't think that very much else could be rationally justified either, and the running theme of his philosophical works was the thesis that our belief-system, right across the board, is not grounded in any philosophical arguments at all, but rather in our passionate impulses and habits. So he still left plenty of room for religious faith, as such, but merely wished to show that the Argument from Design could do nothing to underpin such faith. Most philosophers nowadays would, I think, agree with him on this.