Deuteronomy 22:11 defines shatnez as wool and linen. But cotton wasn't available then. If cotton is fine then that would also mean a cotton garment with leprous disease would be fine since it is not included in Leviticus 13:47-48. Should shatnez include cotton? Does shatnez really mean to imply not mixing animal and vegetable fibers?
The logic about tzara'at (let's assume the flawed translation of "leprosy") actually flows the other way -- in fact, the Torah specified "wool, linen, and leather", and it applies only to those materials.
Maimonides, Laws of Leprous Afflictions 13:1--4:
יג,א אין מיטמא בנגעים אלא בגדי צמר ופשתים בלבד, או השתי או הערב של צמר ופשתים, וכל כלי העור, ...
יג,ג צמר גמלים וצמר רחלים שטרפן זה בזה--אם רוב מן הגמלים, אינו מיטמא בנגעים; ואם רוב מן הרחלים, מיטמא בנגעים; מחצה למחצה, מיטמא בנגעים. והוא הדין בפשתן וקנבס שטרפן זה בזה. ורחל בת עז, אין צמר שלה מיטמא בנגעים.
יג,ד בגד שהיה שתייו פשתן וערבו קנבס, או שתייו קנבס וערבו פשתן--אינו מיטמא בנגעים;
The only garments that become contaminated via afflictions are wool, linen, wool or linen thread, or any leather garment ... if one blended camelhair and sheep's-wool, if the majority is camel, the garment is not susceptible to impurity by affliction; majority sheep, it is, half-and-half, it is; same for a blend of linen and canvas; nor does the wool of a sheep-goat hybrid qualify.
The Torah picked some very specific materials for certain commandments, and it applies only to those. It's not our place to assume we know why and then extrapolate out to new prohibitions.
(On Shaatnez -- note that Abel's sacrifice was a sheep, while the midrash tells us that Cain's plant-sacrifice was linen -- so those two don't mix. Except in the high priest's uniform, but that's another question ...)
It's not about "was the substance known at the time" -- goat hair clearly was known, for instance (used in the Tabernacle, and called simply izim ["nanny-goats"], never "wool"), yet the Torah chose to specify wool and linen. If the Torah wanted to use general language it could certainly have done so -- for instance in Deut. 23:20 "don't take interest from money, not from food, not anything you would use for interest!" -- it could have written "any thread you spin from animals or plants", yet it chose not to.
The full blessing for "bread", for example, only applies to five Biblical grains. There's some fascinating discussion on whether the laws of contamination via metal apply to all metals, or only those specified in Numbers 31:22 -- the Torah could have used some generic description of metals -- "anything you heat and shape" or the like. (This actually comes into play with kohanim, who are to avoid contamination-via-corpses, flying over cemeteries; the standard airliners are made of aluminum or composites.)