The cause for the change was because in the time of the Talmud both single and married women went to the mikvah after becoming a nidda, thus it was the norm to be in that state of impurity, and had no connotation of intimacy, it simply was a process to purify oneself in order to either partake of Terumah or to enter into the Temple to bring a sacrifice, thus there was a "plausible deniability" as to why a woman was going to the mikvah.
However today, since we do not observe the laws of ritual impurity, and going to the mikvah became exclusive for married woman who went to become permissible to their husbands, it became that going to the mikvah and intimacy have become enmeshed as one; therefore, for modestly purposes it became the norm to act discreetly so as not to publicize the fact that in all likely hood this woman will be having relations with her husband. Despite the fact that we may know it intellectually that most couples are together on a monthly basis nonetheless to activly draw attention to it is a grave sin as the Gemara in Shabbos 33a:
א"ר חנן בר רבא הכל יודעין כלה למה נכנסה לחופה אלא כל המנבל פיו אפי'
חותמין עליו גזר דין של שבעים שנה לטובה הופכין עליו לרעה
The Sefer Ikkrei Dinim (Yoreh Deah Siman 21) in discussing the question of a Chuppas Nidda - a bride who is in Nidda. May the Chosson place the ring on her finger which will inevitably lead to touching her? Or must he slightly place it on her finger being careful not to touch her (as is the opinion of the Maharil quoted in Be'er Hetev Even Haezer [61:8]) writes that the minhag is not to be concerned as we do not want to publicize that she is in Nidda.