IS there an answer to this question?

Hirhurim poses the question, "Why do we do Mitzvos?" and then gives an answer.

I'm not going to debate whether his answer is correct. Rather, my belief is that the question has a flawed premise.

Take a different, but similar, question: Why be moral?
Here also, a lot of ink was spilled trying to give an answer. Until developmental psychologist Lawrence Kohlberg and his researchers began to pose 'moral dilemmas' to children of all ages, and analyzing the answers.
In a nutshell, he demonstrates that human beings progress through distinct levels of moral development (you can find a summary here). He (being a secular humanist male) was pretty monistic about where those stages led. Critiques, starting with Carol Gilligan's classic feminist critique 'In a Different Voice' (written, actually, as a response to Kohlberg) posited alternative hierarchies to Kohlberg's moral development. She succeeds in demonstrating why, in Kohlberg's experiments, women were strangely coming up more morally underdeveloped than men, but also essentially accepts his premise of a constrined moral development in humans.

Doing Mitzvot because God commanded is what Kohlberg would call stage 4, which is part of 'conventional morality'. Doing things because it's the law, not because of how you'll be percieved, or to gain reward, but because the law itself is important. At this stage, one wouldn't ask the question "But why obey?".

We can ask that question to R' Gil's answer - OK, God decreed mitzvot upon us. So? Why should I obey?
The conventional moral thinker wouldn't absorb the question. Preconventional thinkers would say things like 'Because then I'll get candy in Olam Habah', etc.

But if Kohlberg's right, there are still stages beyond this; we might not accept his definitions of those stages, or at least not define them as narrowly as he does, but there is something beyond.

For example:
In Stage 5, the reason for doing the mitzvot would be to maintain my covenantal relationship with God, a strong identification with God which generates a desire to carry out his will as a function of love.
I'd suggest that the Torah's 'stage 6' would correspond to 'Halicha Be-drakhav', imitation Dei, where my actions are determines by a desire to become more Godly, to live up to a moral Ideal. Interestingly, here the machloket between Gilligan and Kohlberg is whether that ideal is compassion or justice, whereas Chazal recognized 13 separate 'ideals' heare - 'Just as He is called 'Compassionate', so to shall you be compassionate...'.
Perhaps a 7th stage (and here we move beyond Kohlberg) would mean that asking 'why do you do Mitzvot?' is like asking 'Why do you breathe?' - it's the most normal, intuitive, authentic thing to do. It's the true expression of my soul, which is itself a spark of the Divine. Here, the doors to the soul are completely thrown open, such that there's no percieved imposition, no barrier at all, between my own will and God's Will - because no separation is perceived. This stage is desribed in Jewish literature, especially in late 19th/early 20th century Polish Chassidut, as a complete loss of self-consciousness.
There may even be a further stage where one relates to him or herself completely as an expression of Divinity, reaching beyond conventional categories of good and evil and envisioning all as pure expression of God's Will. Let's just say that not too many folks reach high enough on the ladder to be taken seriously when they talk about 'aveirah lishmah'. Maybe the Amshinover Rebbe. Some would say Shlomo Carlebach. In general, there's a lot of danger when people start relating as though they've acheived higher stages when they haven't. Ve-acamo"l.

Maybe I'm being a bit too monistic even within a Jewish view of moral development. Maybe some of the stages can manifest themselves in different ways even within a Halakhic perspective. Maybe similar experiences are understoof or 'unpacked' differently by different people. We'll let the good folks at Lookjed worry about that.

For us, though, it's important to recognize that the answer to R' Gil's question changes as we change, that we don't expect young children to give the same answer as adults, and that as long as we're still 'baynonim' (as the term is used in Tanya) we should hope that our answer will continue to change, and that we remain dissatisfied with 'level 4'.