The amoraim forbade yibum a long time ago. In all cases of yibum since the time of the gemara, chalitza is performed. This is not the same as polygamy. Communities that did not accept Rabbeinu Gershom’s cherem always allowed it, assuming the host country’s laws were OK with it (not too common nowadays).
Avadim: there are many opinions among the Rishonim on this. According to some, it could only be reinstated when we get back the Yovel, which clearly no one is claiming today to fulfill.
Tzara’as: see interesting remarks on this at the end of the Tiferes YIsrael’s lengthy hakdama to Mishnayos Negaim. He wrote that in his youth, he asked Rebbe Akiva Eiger why the halachos of tumas tzara’as are not practiced nowadays. Rebbe Akiva Eiger told him that’s a very good question and he doesn’t have a good answer. The Tiferes YIsrael continues that when he got a bit older, he decided that it’s because we don’t have kohanim me’yuchasim. He bases this on a Rambam in HIlchos Terumos, I beleive the Minchas Chinuch also writes that same reason — because of the Rambam.
Korbanos: it’s mainly because of tumah, although there are many other considerations, such as the precise makom ha’mizbeiach (the dimensions of the Har Habayis has changed over the past 1900 years), bigdei kehuna, and others. The only question we could ask is about Korban Pesach that could be brought bi’tumah. On this (like on all other matters) we rely on the knowledge of our gedolei Torah who are not clamoring to do it. May we be zoche to do it in our days!