In Rashi's second explanation of Behaaloscha 12:12, he says
אִם אֵינְךָ רוֹפְאָהּ בִּתְפִלָּה, מִי מַסְגִּירָהּ,מִי מְטַהֲרָהּ? אֲנִי אִ"אֶ לִרְאוֹתָהּ, שֶׁאֲנִי קָרוֹב וְאֵין קָרוֹב רוֹאֶה אֶת הַנְּגָעִים, וְכֹהֵן אַחֵר אֵין בָּעוֹלָם, וְזֶהוּ אשר בצאתו מרחם אמו:
if you don't cure her through prayer, who will quarantine her and who will make her pure again? I can't, because she's my relative and a relative can't rule about tzaraas [this is Rabbi Meir's opinion; we don't rule like him], and there's no other Kohen in the world to do it.
But someone with tzaraas doesn't become tamei until a Kohen proclaims him so. If there's no Kohen eligible to do it, there are no halachic consequences. So what's the problem?