The cause for Metzora

In the time of Chazal, there was already no actual Metzora. No one had these skin conditions, and no one was declared tamei. Rather, it was in the realm of drosh ve-kabel schar.

So, when Chazal say something like this:

Then the kohen shall order, and the person to be cleansed shall take two live, clean birds, a cedar stick, a strip of crimson [wool], and hyssop.

ד. וְצִוָּה הַכֹּהֵן וְלָקַח לַמִּטַּהֵר שְׁתֵּי צִפֳּרִים חַיּוֹת טְהֹרוֹת וְעֵץ אֶרֶז וּשְׁנִי תוֹלַעַת וְאֵזֹב:

clean [birds]: Excluding an unclean bird, [i.e., forbidden to be eaten] (see Chul. 140a). [Why are birds required for this cleansing rite?] Because lesions of tzara’ath come as a result of derogatory speech, which is done by chattering. Therefore, for his cleansing, this person is required to bring birds, which twitter constantly with chirping sounds. — [Arachin 16b]		טהרות: פרט לעוף טמא. לפי שהנגעים באין על לשון הרע, שהוא מעשה פטפוטי דברים, לפיכך הוזקקו לטהרתו צפרים, שמפטפטין תמיד בצפצוף קול:
a cedar stick: Because lesions of tzara’ath come because of haughtiness [symbolized by the tall cedar]. — [Arachin 16a]		ועץ ארז: לפי שהנגעים באין על גסות הרוח:
a strip of crimson [wool], and hyssop: What is the remedy that he may be healed [of his tzara’ath]? He must humble himself from his haughtiness, just as [symbolized by] the תּוֹלַעַת [lit., “a worm,” which infested the berries from which the crimson dye was extracted to color wool], and the [lowly] hyssop. — [Tanchuma 3]		ושני תולעת ואזב: מה תקנתו ויתרפא, ישפיל עצמו מגאותו, כתולעת וכאזוב:

it is good to note that they weren't pointing to a specific person and saying to him / about him that his suffering was due to his own sins, and that these were the specific sins he was guilty of.

Rather, it is taking a somewhat dry and technical area of halacha with no present-day application and, besides of course discussing the actual laws, moving it to something which people could relate to and derive important life lessons from. Namely, that one should not be haughty, or say lashon hara. And then, for whatever major or minor ills, one can engage in introspection and cure oneself by working on one's middos. I don't think they really intended people to engage, regularly, in extrospection -- "that person is suffering from those ills because he is a bad guy."

And meanwhile this is different from the sense one might have arrived at by looking at the plain text, in which we don't know why this person got this affliction, there is this unknown spiritual / physical malady, and it is in the hands of the Kohen to pronounce him in one state of the other.

(Sure, they have Biblical precedent for this. For instance, Miriam, who told lashon hara. But firstly, we might consider that a specific instance of Divine wrath, rather than something from which we can extrapolate from.)