Notes on Acharei Mos
Aharon's sons died because they approached G-d from pure spirit and did not tie it back to physical acts as symbolized by their entering Holy of Holies, not wearing all the proper garments, not marrying or having children (Midrash). Mitzvos are garments of the soul.
Blog note: this can explain why even if limud Torah has special properties that mitzvos don't have we still need to do mitzvos. Hashem wants us to rectify, bring holiness into the world and we need mitzvos for that. The Baal HaTanya explains that Torah study brings the soul closer to Hashem but mitzvos bring the sechinah into the world and that is our purpose, to make the world a dwelling place. This is why mitzvos displace Torah study if there's nobody else around to do the mitzvah. Why can the mitzvah be done by another? Because the important thing is that somebody does it. The goal concerns Hashem.
Lubavitcher Rebbe
R' Avigdor Miller explains that our goal is to become an eved Hashem and for that we need to use our free choice to surrender our free choice to do His will. (YK note: the mitzvos are His will. How can you be an Eved if you are not doing anything.) He says we must learn from the mitzvos and not just do them.
See also Tehillim 119 on the love for commandments.