Here is a shiur that discusses towards the end [among other things] Tvilas Ezra. After asking mechila from the distinguished lecturerer [and the father of my shadchanit], I feel compelled to comment as follows:
According to many early sources [Rav Hai Gaon, R' Chananel, Rabbeinu Yona, Rosh and many, many, many others] the takana of Ezra was only cancelled for Torah but not for tfilla. [There is also an opinion that it was cancelled for tfilla and not Torah]. According to these authorities, one is obligated to immerse in mikva before davening [if one is a baal keri]. The Rambam famously writes in a letter that he NEVER MISSED A TVILAS EZRA in his life. So it eludes me how "Briskers" can flippantly dismiss the idea of following Takanas Ezra. Of course the Shulchan Aruch rules that one may be lenient but that doesn't negate the opinion of so many rishonim.
And the logic that if people go for tvilas ezra they will feel compelled to go every day so that people don't know that they are Baalei Keri is odd. I don't know where it says this and the fact is that plenty of people are careful about this tvila and don't feel compelled to go every day. Women go to mikva even though people in the mikva know what that means – men should be no different.
And here is a chiddush that most people don't know that I add as a treat: The Kesef Mishna writes [Tefilla 4/4] that Takanas Ezra was never abolished! Since it didn't spread it became non-obligatory but there is still a kiyum every time one keeps it. Ayain shom!!
That is from a strictly halachic perspective. From the perspective of Avodas Hashem, the holy Maor Va-shemesh [Emor] writes:
שא"א לו לאדם שישיג תכלית יראת ה' אלא אם נזהר בטבילת עזרא והי' העולם שמם עד שבאו שני המאורות הגדולים לעולם הבעש"ט הק' ואדמו"ר הרב ר' אלימלך נבג"מ והם פתחו שער לד' צדיקים יבואו בו שלא יהרהר אדם שום הרהור תורה עד שיטביל עצמו לקריו.
It is impossible to achieve Yiras Hashem if one is not careful about Tvilas Ezra.
The Holy Rebbe R' Schneur Zalman of Liadi writes [Likkutei Torah Ki Savo] about tevilah before tfilla [even when one is not a baal keri]
וקודם התפלה צריך כובד ראש, שהוא המרירות על שאין בחי' ישראל לי ראש, וזהו בחי' כובד ראש והיינו שיבא לידי הכנעה והשפלות ופחיתות עצמו במוח בידיעה היטב. וג' דברים הם להסיר כל המונעים בתפלה א' מקוה וכמו שמצינו במשנה פ"ח דיומא מה מקוה מטהר הב' צדקה והג' הוא עסק ולימוד דברי מוסר ובפרט דברי מוסר הנמצאים בזהר מלשון הארה.
He says that before davening one should engage in 3 behaviors in order to achieve the requisite כובד ראש ["heavy head"] that is mandated by the mishna. Mikva, tzdaka and learning pnimiyus hatorah. [See חסידות מבוארת on tfilla for an explanation of this passage]. There are many sources extolling the virtues of the added purity afforded by going to the mikva daily [or at least often]. We live in a very impure world, we are surrounded by immodesty wherever we turn. Anything that adds purity is the call of the day.
