What is the Purpose of Mitzvos? To Teach Us To Be Lenient, Merciful and Kind?

This evening I learned the following chapter in the Guide for the Perplexed with my chavrusa, Rabbi Avraham Garfinkel:

The laws concerning the relation between lender and borrower" (Hilkhos Malveh veLoveh) will be found, on being carefully examined, to be nothing but commands to be lenient, merciful and kind to the needy, not to deprive them of the use of anything indispensable in the preparation of food." No man shall take the nether or the upper millstone to pledge: for he taketh a man's life
to pledge" (Deut. xxiv. 6)…

Mercy is also the object of the law," Thou shalt not deliver unto his master the servant that is escaped from his master" (Deut. xxiii. 15): but it teaches besides a very useful lesson, namely, that we must always practice this virtue, help and protect those who seek our help, and not deliver them unto those from whom they flee; and it is not sufficient to give assistance to those
who are in need of our help: we must look after their interests, be kind to them, and not hurt their feeling by words. Thus the Torah says:" He shall dwell with thee, even among you, in that place which he shall choose in one of thy gates, where it liketh him best: thou shalt not vex him" (ibid. ver. 16). This we owe to the lowest among men, to the slave; how much more must we do our duty to the freeborn, when they seek our assistance ?

But, on the other hand, when sinners and evildoers seek our help, it must not be granted; no mercy must be shown to them, and the course of justice must not be interfered with, even if they claim the protection of that which is noblest and highest: for" Thou shalt take him from mine altar that he may die" (Exod. xxi. 14). Here a person comes to seek the help of God, and claims the protection of that which is devoted to his name; God, however, does not help him, and commands that he be delivered up to the prosecutor, from whom he fled. Much less need any one of us help or pity his fellow-men [under such circumstances]: because mercy on sinners is cruelty to all creatures.

These are undoubtedly the right ways designated" righteous statutes and judgments" (Deut. iv. 8), and different from the ways of the fools, who consider a person praiseworthy when he helps and protects his fellow-men, without discriminating between the oppressor and the oppressed. This is well known from their (i.e. Muslim) words and songs.
--(Guide, III,39)

Rabbi Garfinkel concluded from this that the purpose of the mitzvos is to inculcate in us these character traits of kindness and mercy.

A question I have is based on a discussion of the ta'amei haMitzvos in the book, Halakhic Mind, by the Rav, R. Joseph B. Soloveitchik. The Rav writes in Halakhic Mind that the usual understanding of ta'amei hamitzvos is the attempt to rationalize commandments according to logic or common sense or ethics. The problem is that mitzvos have a logic all their own that may not appear to be rational by any other standards or become oversimplified to the point of unimportance when rationalized. The question should not be: Why is this a mitzva? Or, how is this a mitzva? Rather, the questions should be: What is the halakha? Even if it confounds normal reasoning, what does the mitzva teach?

In the Rav’s words:

For example, should we posit the question: why did God forbid perjury? The intellectualistic philosopher would promptly reply, “because it is contrary to the norm of truth.” Thus he would explain a religious norm by an ethical precept, making religion the handmaid of ethics. Again, when the same philosopher attempts to sanction dietary laws on hygienic grounds, the specific religious content and meaning are supplanted by a principle of foreign extraction. If the Sabbath is to be seen only against the background of mundane social justice and similar ideals, the intrinsic quality of the Sabbath is transformed into something alien. It serves merely as a means to the realization of a “higher” end. Maimonides’ efforts foreshadowed failure from the very outset of his “how” approach.

It is worthy to note that Maimonides, the halakhic scholar, came nearer the core of philosophical truth than Maimonides the speculative philosopher. In contradistinction to the causal method of the philosophical Guide (the Mishne Torah) apprehends the religious act in an entirely different light. The Code does not pursue the objective causation of the commandment, but attempts to reconstruct its subjective correlative. It would seem the Maimonides of the Halakha was not intrigued by the “how” question. He freed himself from the generic purview and employed a descriptive method of expounding the content and symbolic meaning of the religious norm. The “what” question was his guide in the Code.
--R. Joseph B. Soloveitchik, Halakhic Mind, (New York: Macmillan, 1986), pp. 93-94.

The Brisker's in general claim that one cannot ask "why" about mitzvos but only "what".
The Beis Halevi mentions this idea in Parshas Bo, on verse 12:26 (page 119 in the new edition of the Beis Halevi, starting on paragraph Vihegadita livincha bayom). (In short) He says the wicked son of the Hagadah is someone who will not do a mitzvah until he understands the reason behind it. He contrasts this to the wise son's question about the laws of Pesach (this is the idea of what not why). He says making up reasons for mitzvos is a bad idea because when one of those reasons doesn't apply, people will say the mitzva is obsolete.

Perhaps the original source for this Brisker approach is in Berakhos 33a where the Mishnah says, IF ONE [IN PRAYING] SAYS ‘MAY THY MERCIES EXTEND TO A BIRD'S NEST’ ...HE IS SILENCED. and the Gemara adds: But what is the reason for silencing him if he says ‘THY MERCIES EXTEND TO THE BIRD'S NEST? — Two Amoraim in the West, R. Jose b. Abin and R. Jose b. Zebida, give different answers; one says it is because he creates jealousy among God's creatures, the other, because he presents the measures taken by the Holy One, blessed be He, as springing from compassion, whereas they are but decrees....[emphasis mine]

I believe the Rambam uses both approaches: why? and what? The Rambam is teaching us the value of both approaches to understand the Torah more fully. The questions are not mutually exclusive. Rather, they complement each other.