Rav Einstadter shlit"a gave a wonderful presentation on the mitzvah of shemirah by cohanim and leviim in the Mikdash. Can't summarize it all, but:
The rishonim in the gemara all say it is a matter of kavod to the Mikdash. But the Torah everywhere in Bamidbar explains that וזר הקרב יומת - the idea of shemirah is to keep the zarim out. This is also the way the mitzvah is explained by the Gra and Likutei Halachos, and is part of the keser in the Rambam.
One nafka minah would be that you'd need to guard in the day, even more (maybe) than the night.
The rishonim don't seem to mention this explanation at all.
Rav Einstadter wanted to explain that there are many parts of the Torah, especially in Bamidbar, which are mitzvos for the Mishkan but not l'doros in the Mikdash. This might be one of them; then you need to explain why the idea of kavod for the Mikdash is in the Torah as well, and why keeping zarim out only applied in the Mishkan (which he discussed).
The rishonim in the gemara all say it is a matter of kavod to the Mikdash. But the Torah everywhere in Bamidbar explains that וזר הקרב יומת - the idea of shemirah is to keep the zarim out. This is also the way the mitzvah is explained by the Gra and Likutei Halachos, and is part of the keser in the Rambam.
One nafka minah would be that you'd need to guard in the day, even more (maybe) than the night.
The rishonim don't seem to mention this explanation at all.
Rav Einstadter wanted to explain that there are many parts of the Torah, especially in Bamidbar, which are mitzvos for the Mishkan but not l'doros in the Mikdash. This might be one of them; then you need to explain why the idea of kavod for the Mikdash is in the Torah as well, and why keeping zarim out only applied in the Mishkan (which he discussed).