Does the oral tradition that identifies the hilazon as the source of tekheles necessarily indicate that one could not create the indigo-colored wool by other means? The gemara certainly indicates that the color-equivalent, plant-derived kala ilan is not valid (e.g. Menachot 40a, 43a, Bava Metzia 61b) but it also implies that this particular dye was not as fast and permanent as true tekhelet (and therefore, implicitly, was not its molecular equivalent). If that is the case, if one was able to create a dye that was chemically indistinguishable from true tekhelet, considering that torah shebiksav (the Written Law) never explicitly mentions the source of tekhelet, might that not also be acceptable?
This requirement is stated in the Tosefta and Meseches Tzitzith
Tosefta Menachoth 9:16
"תכלת אין כשרה אלא מן החלזון הביא שלא מן החלזון פסולה."
Tekheleth is only valid from the חלזון ; if one used a dye not made from the חלזון it is invalid.”
מסכת ציצית פרק א הלכה י
שאין צובעין תכלת אלא בחלזון.
We only dye תכלת with a חלזון
R. Yisrael Lipschitz writes the following in his introduction to Seder Moed:
הכלל העולה דבין ציצית ובין בגדי כהונה א״צ חלזון דוקא אבל צריך בשניהן שיהיה מראה (היממעלבלויא) שאינו משתנה מיפיו ע״י בדיקה שהזכיר הש״ס
The principle that emerges is that both by tzitzit and by the priestly vestments it is not necessary to specifically use a chilazon. But it is necessary by both that the color be sky-blue that does not deteriorate from it’s beauty via the test mentioned in the Talmud.
R. Joseph Ber Soloveitchik (as recorded in שיעורי הרב הגאון רבי יוסף דב הלוי סולוביצ׳יק זצ״ל על עניני ציצית עניני תפילין והלכות קריאת התורה) reached the same conclusion:
ובה״ב כיצד צובעין תכלת של ציצית לוקחים וכו׳ דם חלזון וכו׳ אבל בה״א לא הזכיר חלזון כשהגדיר מהו התכלת רק בה״ב כשהזכיר איך עושים אותה בפועל ומשמע דלא הוי חלזון הללמ״מ אלא שבמציאות הוא הי׳ הצבע היחיד שהי׳ מתקיים שהי׳ עינו השמים והים אבל איה״נ דאילו הי׳ לנו בזה״ז צבע סינטטי אחר שהי׳ מתקיים הי׳ כשר לתכלת
And in Law 2: “How do we dye the techeilet of tzitzit? Take... the blood of the chilazon...” But in Law 1 chilazon is not mentioned when techeilet is defined; only in Law 2 when mentioning how to actually make it. This implies that chilazon is not a law to Moses from Sinai; rather, it was in reality the only dye that was steadfast whose color was [that of] the sky and the sea. But indeed if we had nowadays another synthetic dye that was steadfast it would be valid for techeilet.
(Elisions in original)
One interesting point. The Tiferes Yisrael points out in his introduction to Seder Moed regarding the Bigdei Kehuna (where some clothes require Techeiles):
goes even further and questions the need for chilazon at all. He sees no reason to differentiate the techeiles of tzitzis from the techeiles of the priestly garments since the Torah uses the same word in both cases. He concludes that as long as a blue dye is the correct shade and is colorfast then it should meet the Torah's requirements. However, after consulting with expert dyers of his day, Tiferes Yisrael discovered that there did not exist any blue dye known at that time that was sufficiently colorfast.
[Tiferes Yisrael was certainly familiar with plant-based indigo, for he identifies kala ilan as indigo. Apparently he felt that the indigo of his day was not colorfast enough to pass the strict chemical tests described by the Gemara.]
He concludes that, for practical purposes, the only way to obtain techeiles must be from a chilazon. Had Tiferes Yisrael been shown the indigo of today, which is certainly colorfast, he would likely agree that it would serve as techeiles both for tzitzis as well as the priestly garments.
The above stated, he's the only one hypothetically supportive of Kala Ilan used for Techeiles. Virtually everyone else disagrees with him.
The Tiferes Yisrael statement is quoted by Alex above, but this comment fleshes the idea out more.