You ask, "let's say that Murex is not the chilazon, and we have some strings that have been dyed blue for no reason. What's the problem with that?" (my emphasis)
If there really is no reason to dye them blue whatsoever, then doing so would be a violation of the Shulchan Aruch (9:5), who says that careful people use strings of the same color as the garment, and we use a white garment, and the Rama there who notes that the custom is to use white (this is pointed out by R. Elyashiv in his collected teshuvos, 1:2). While the Chazon Ish (3:25) and the Radziner Rebbe (Ein HaTecheiles 1:40:1) don't think that this applies to all of the strings, many poskim seem to assume that all four strings should be white, in the absence of techeiles.
This stringency, however, would not be enough of a reason to say not to use techeiles if there's any reason at all to assume that it might be correct.
Let's assume, then, that it's a matter of doubt, and (the assumption is) that one should be stringent as ספק דאורייתא לחומרא. Why not dye them with the new blue?
A halachik reason: Many (including R. Moshe Shternbach, Teshuvos V'Hanhagos 1:26 and 4:5) have written that placing something extra on tzitzis with the intent to possibly perform a mitzvah, even out of doubt, is violating the prohibition of bal tosif. (This is the indication of the Gemara in Zevachim 81a, and though the Ritva Sukkah 31b says otherwise, there were many poskim throughout history on both sides of this question).
A kabbalistic reason: There are apparently kabbalistic reasons to avoid using real techeiles strings nowadays anyway, which was the objection of R. Yisrael Yehoshua Trunk (Shu"t Yeshuos Malko O.C. 1-3). (It's hard for this to be understood literally as Kabbalah can't uproot a biblical obligation. Rav Asher Weiss suggests the intention might be more along the lines of: kabbalah tells us that the true techeiles has been lost and so anyone who thinks they are wearing it nowadays must be donning a spiritually destructive fake.)
A meta-halachik reason: I've been told by a posek that he was worried that if we come to dye them blue from the murex out of doubt, then future generations might mistakenly believe that there's a tradition that this is the proper chilazon. This is problematic because (1) it is a 'ziyuf hatorah', a misrepresentation of the Torah, which the Maharshal (Yam Shel Shelomo B.K. 4:9) thinks is so terrible as to be worth dying for (2) if Eliyahu does come and provides us with a different snail, things could get very awkward and we might not know what to do.
If you are going to wear it in public, then we can add that R. Shternbach (ibid.) prohibits wearing blue tzitzis in public because of the prohbition of 'lo tisgodedu', of making apparent divisions in halakhic practice among different people.
Of course, the assumption above that there is a formal halachik doubt here is debatable as well. R. Shternbach (ibid.) writes that something without a tradition cannot even be considered a safek. Also, R. Soloveitchik (Shiurim L'Zecher Abba Mori, pg 228) as well as several others quote the Beis Halevi (though there is some debate if he actually said this) as saying that something that has been lost to tradition is equivalent to a tradition that something has been lost; meaning, it's as if there's a mesorah not to use anything as blue until Eliyahu or the like can reinstate it from their own mesorah, not just from arguments.
Additionally, it isn't at all true that the evidence is 'compelling' to everyone that the murex trunculus is the correct fish for dying techeiles. There are good answers to this question, both in terms of archaeological evidence and halakhic literature regarding the identity of the chilazon. Rav Asher Weiss and Rav Shlomo Miller, both widely accepted poskim, do not think that there is enough evidence to even raise a doubt, and discourage the use of techeiles (without really providing an answer to this question). For many people, the fact that these poskim are unconvinced is enough of a reason not to view it as a doubt. (The list of poskim that have discouraged it extends far beyond these, though of course it isn't unanimous, and those who do wear techeiles have answers to the above issues. You asked about the potential downsides).
