Shu"T Mahara"Ch Ohr Zaru'a 128 raises three very fundamental questions:
1. Since there is a din of mitzvah bo yoseir mi'bshlucho, why isn't anyone careful to shecht his own meat or be mafrish challah (apparently the common practice was to appoint a shliach to do so)?
2. How can a shliach say a bracha on shechita or hafrashas challah when the shliach has no mitzvah to shecht the animal or be mafrish challah from that dough -- the mitzvah is on the owner?
3. Why can you appoint a shliach for a mitzvah like hafrashas challah but not for a mitzvah like putting on tefillin or eating matzah?
He makes a few important distinctions:
A. Shechita and hafrashas challah is different than tefillin and matzah because in the former cases all we care about is the end result, i.e. knowing that the food was properly prepared through slaughtering or through hafrasha being done. In the latter case, it's the process, the putting on of the tefillin, consuming the matzah, which is important. (See his hesber of why you can appoint a shliach for gittin/kiddushin but not chalitzah and compare with Tos Kesubos 74a d"h tnai.)
B. Mitzvah bo yoseir mi'bshlucho applies in the case of kiddushin because the one performing the mitzvah has everything to gain and nothing to lose, as opposed to the shliach, who gains nothing, and loses the ability to marry the kallah. It's a one sided deal. When it comes to shechita, hafrasha, other mitzvos, neither the shliach or the m'shaleiach has a greater or lesser stake in the outcome.