The Rogatchover points out that the issue of whether the Mishkan served simply to enable hakravas korbanos or whether it had an independent function as the dwelling place of the Shechina may underly a dispute in the Yerushalmi (Shekalim 4:2 - 16b):
א"ר חזקיה תנא רבי יהודה נדנניות השלחן והמנורה והמזבחות והפרוכת מעכבים את הקרבנות דברי ר"מ וחכ"א אין לך מעכב את הקרבן אלא הכיור והכן בלבד
According to R' Meir all of the kelim of the Mikdash must exist and be in place before korbanos can be offered; a completely functional Mikdash is a necessary ingredient of hakravas korbanos. The Chachamim disagree -- the building of Mikdash and the offering of korbanos are two completely seperate functions.
We end the song of dayeinu with the hope of the rebuilding of Mikdash "l'chapeir al kol avaonoseinu", to atone for our sins. Technically it is not the Mikdash which serves as a kaparah, but the korbanos in the Mikdash. This line of the piyut seems to support the view that the Mikdash is itself necessary to bring korbanos properly, similar to the view of the Rambam.