He was not religious but he saw that Torah was an important source of value. But he was also aware that the problems of the Enlightenment did not pop up spontaneously. They had arisen as the problems with Throne and Altar in the Middle Ages had become apparent. That is he did not see any essential workable approach at all. And he thought that unless one was found we are all in hot soup.
That being said I should mention that I thought I had seen something amazing in the Litvak Yeshiva world. But I also saw the surrounding religious world is a kind of insane asylum. So I saw I kind of solution to the problems that Allen Bloom saw. --that is to learn and keep straight Torah. But I also saw that the religious are mad. So It seems to me there is a simpler solution simply to join a Reform Temple or a Conservative Synagogue and to learn Torah in that context or on ones own.
That I I would avoid the religious at all cost unless there happens to be a legitimate Litvak yeshiva in the area. That is any yeshiva based on the Gra, Reb Israel Salanter and Rav Shach. For example: Ponovitch, Mir, Brisk, Chaim Berlin, Torah VeDaat and others based on that model.
To explain why I think avoiding the religious at all cost is important I have to make note that the major mitzvah in the Torah is to avoid idolatry. Since every religious group that I know of is heavily into idolatry it is therefore important to avoid them. That takes precedence of any kind of benefit you imagine you might gain from them.
I think Dr Bloom was thinking along the lines that Hegel would be an answer to the kind of dilemma he was seeing, but if he thought so why did he not write it openly? Same goes for the Oral and Written Torah. Why did he not say so? The only openly expressed answer in his entire book is for people to learn the Republic of Plato. [Read between the lines and you might see that Dr Bloom was also considering the three critiques of Kant. But he clearly was not going to choose between Kant and Hegel. If anything he would have suggested reading and learning intensely both.
The Alt Right is suggesting a return to kings but not to Altar.(the Catholic Church). They are also suggesting nationalism.
Both seem very close to Hegel with his Constitutional Monarchy and importance of the super organism. I however have a lot of trouble with Hegel.
But at least Dr. Bloom and I agree on the importance of Plato and Kant and see the importance of the Law of Moses.
I am personally in favor of Plato and the whole Kant/Hegel school which is highly Platonic. Christians I think are not very happy with Plato because of the heresies of the Gnostics like Valentinus.