Parshas Vayeishev provides the paradigmatic event of “too much tznius”: maaseh Yehuda v’Tamar.
The medrash relates just how Tamar was able to seduce her father-in-law Yehuda: she have covered her face while in his house and so he did not recognize her when he saw her. This behavior is simultaneously praised and condemned at the same time in Bereishis Rabbah 85:9; Bereishis Rabbah 35:8 goes so far as to acknowledge the possibility that one might become overly unfamiliar with (the looks of) one’s female relatives to the point that disaster may result.
(This is more prevalent than one might think; I know personally of a scion of a prominent Chassidic family who lost the chance at a shidduch because he refused to look at his potential mother-in-law.)
In her “A Return To Modesty”, Wendy Shalit relates how Muslim men are actually “turned on” by women in the chador. I remember more than one aspiring rabbinic student saying that the most beautiful thing about a woman is her ankle-length skirt. Ironically, it is the use of the veil itself—which Ramban relates was a tool of the trade of both common (zonah) and sacred (kedesha) prostitutes—which allows Tamar to succeed. Almost a "bizarro tznius", as it were.
Even regarding the “icon” of tznius—Bas Kimchis, who merited to have seven sons become High Priest during Temple times, who, according to the Gemara, is supposed to exemplify “Kol Kevuda de-Ba Melech Penima” because “the beams of her house never saw the braids of her hair” (Yoma 47a) —there might be, or lack of a better term, less than meets the eye.
Rabbi Yossi (Yoma 12b) notes that a Kohen Gadol could be reinstated following his purification, but his (temporary) replacement was stuck with all the restrictions and none of the privileges of his previous position, because of “maalin bekedusha”. The gemara further (ibid 47a) details just how the series of disqualifications and elevations to the position occurred among the brothers: being hit by Gentile spittle. Additionally, the gemara notes that while "she credited her success to her modesty,  the Chachamim indicated that others had done similarly but had not merited such honor"
leading one to re-examine Bas Kimchis’ rewards, and, by extension, though not to take away from her piety, how desirable her conduct really was from an educational standpoint.
In another example of tznius short-circuiting itself, Batsheva, says the Midrash, even when she washed her hair, she had her attendant hold a towel over her hair so that it not become overly exposed, even IN HER HOUSE. King David, shooting at a bird and missing, instead hit the towel and caused Bas Sheva's hair to become temporarily revealed. We all know the immediate aftermath.
In Tamar’s case (who, less than coincidentally, was a Bas Kohen), we can take the too much tznius theme a step further by what happens to her in Yehuda’s house before she feels compelled to seduce Yehuda. This is the famous maaseh Er v’Onan, which became a catchall for shichvas zera levatala (another educational misnomer, but I’m not going to deal with that here). However, the real capital offense here, according to Tosfos in Yevamos 45b and Chizkuni here in the parsha, was exclusive biah shelo ke-darka, and one can surmise that it was nonconsensual. There doesn’t seem to be any solid scriptural or midrashic evidence to this effect, but the circumstantial evidence-- Tamar’s tznius and the fact that she lived while both brothers died—is pretty strong.
One might even view the entire plot from the seduction through Yehuda’s “tzadka mimeni” as Tamar quietly indicting Yehuda for the way he ran his household—specifically, how tznius was at such a premium in a household where sexual deviancy was rampant—and how Yehuda “blamed the victim” by withholding Tamar from Shela because he thought she was responsible for Er and Onan’s deaths.
The parallels to current scandals are obvious.
I have two conclusions after all this. The first is, as I mentioned, that if kol kevuda de’bas melech penima, the benos melech have been mochlos their kavod. Or, to paraphrase author Karen Lehrman, there is no ma’alah involved in being chained to a pedestal.
The second might depend on the degree of which my above statement is descriptive—where there would be no real halachic remedy for the curse of tznius—or prescriptive, in which case one hopes for salient educational approaches to being modest with our modesty.
There is such a thing as too much tznius.