"Any Torah scholar whose inside is not like his outside [whose piety does not match their learning] is no Torah scholar" (Yoma 72b). It is a given that Torah study is meant to make one a better person; more sensitive to the needs of others, aiding in the refinement of character, the development of moral excellence, and greater observance of mitzvoth between man and G-d. Rabban Gamliel went so far as to exclude from the Beit Midrash those scholars whose "inside was not like their outside" (Brachot 28a). Presumably, he agreed with Abaye's assessment that such a person is not only not a scholar, but is "called nitav, an abomination" (Yoma 72b).
Having one continue to grow in learning without a concurrent riseis character risks desecrating the name of G-d. On the other hand, if we deprive people of the opportunity of learning Torah--of 4,000 years of accumulated teaching and wisdom--can we complain if Torah has little impact on them?
Rabbi Elazar ben Azaria--who succeeded Rabban Gamliel as the Nassi, leader of the Jewish people--changed course, allowing all into the Beit Midrash, and 700 benches had to be added on the day of his appointment (Brachot 28b). While this open approach resonates with many, the Talmud notes that Rabban Gamliel and Rabbi Elazar ben Azaria ended up sharing the role of Nassi.
This, Rabbi Soloveitchik explained, teaches us that both approaches have their place; that of restricting Torah to the moral (and presumably intellectual) elite, and ensuring Torah for the masses. The greater the level of learning, the more we must concern ourselves with the person's character.
"And this is the Torah that Moshe put before the Jewish people" (Devarim 4:44). Using a play on words (see Maharsha, Yoma 72b), the Gemara explains that this verse, sung in shuls whenever we read from the Torah, teaches that Torah is both a potion for life and for death--it all depends on how it's used. Torah study that does not inspire awe of G-d and His mitzvoth is Torah study that is sorely deficient. One can master the six orders of the Mishnah, "and even so 'the fear of G-d is its storehouse'" (Isaiah 33:6, Shabbat 31a). Torah is much more than an academic discipline.
Awe of G-d is the precursor to joy, which is another necessary ingredient to proper Torah study. "The commands of G-d are just; they make joyous the heart" (Psalms 19). Torah study is meant to be enjoyable--and this joy precludes a mourner from engaging in Torah study. We are meant to express our joy during Torah study by accompanying it with song, singing being an expression of joy (Megillah 32a).
Those whose Torah study leads neither to awe nor joy are subject to a "double gehinom". As Rashi explains, they miss out on the pleasures of both this world and the next. Viewing Torah as a burden (how sad!), the time spent studying it deprives them of the pleasures of this world. And having no positive impact on them, they risk inheriting gehinom in the World to Come. May we merit to be amongst those who combine awe and joy in our study of Torah.
 Of course, Torah is also an academic discipline, requiring great rigour, exacting standards, the search for truth, freedom of inquiry, and publishing original research, all in a competitive atmosphere.
 The prohibition against a mourner studying Torah may well go beyond the issues of joy. Tosafot, Moed Katan 21a, s.v. Vassur, quotes a debate as to whether a mourner may study the "sad" parts of Torah, something all agree is permitted on Tisha B'Av. Not only a mourner but all who visit a shiva home are proscribed from studying Torah. Torah is a Torat Chaim, a Torah of life. A shiva home is one where death is in the air, and is the antithesis of Torah study, which is a celebration of life.
 This reminds me of Rav Soloveitchik's explanation of Hosea's words that are read on Shabbat Shuva; "Return, O Israel, because you have failed in your sins" (14:2). The Rav noted that often, man can't even sin properly. He may, for example, work on Shabbat, hoping to get ahead, only to watch his shomer Shabbat colleague get the promotion. How tragic when one sins and is so bad at it that he can't even derive benefit from the sin! (See On Repentance, p. 64.)