With the destruction of the Temple, the focus of the seder menu shifted from the eating of the korban pesach to the eating of matza. The importance of eating the korban pesach is such that it carries the punishment of karet, excision, for those who neglect it (along with only one other positive mitzva, that of brit milah). The original paschal lamb was what allowed the Exodus to occur.
One of the unusual laws regarding the korban pesach is that it can only be eaten leminuyav, by those who were specifically intended to be included as part of that particular sacrifice at the time of the slaughtering of the animal.
One of the underlying pillars of democratic thought is confidence in the people to make the right choices, and in leaders to respect those choices. In a healthy democracy, people are well informed, allowing for vigorous debate; and leaders have the best interests of the state at heart. The will of the people is constricted by the Constitution, which reflects the core values that are sacrosanct—and as such, can be changed only with great difficulty and a consensus to do so.
While Korbanot tzibbur, public offerings, were sacrificed on Shabbat and Yom Tov--and serve as the basis for our davening mussaf on these days--private sacrifices were not.
Similar to a public offering, the korban pesach was brought at a fixed time. On the other hand, the obligation to bring such rests on the individual, leading to uncertainty as to whether it may be brought on Shabbat.
Great leaders are great strategists. The Talmud (Pesachim 3b) relates that a certain non-Jew was bragging of how he used to travel to Jerusalem to eat the korban pesach. Under ordinary circumstances, that would be very nice, as non-Jews may also offer sacrifices in the Temple. However, the korban pesach, the pinnacle of celebration of the holiday of the national formation of the Jewish people, is reserved for Jews only. "No outsider may eat it. No uncircumcised male may eat of it" (Shemot 12:43, 48).