The Gemarah says on 12a that according to R' Shimon, that the Zav wearing a Zav's cup to catch the Zevos is a Malacha Shein TZricha L'Gufa. This is because you didn't want the Zeva in the first place and you would rather not have it.
But why is this different than many things that you need because of something you don't want? Carrying an umbrella to protect yourself from the rain, since you don't want the rain in the first place. Or weeding weeds that you didn't want in the first place? Once the unwanted thing is there, it should be Tzricha L'Gufa to bring something to get rid of it
Chaim Smulowitz
The SEFAS EMES asks your question about the umbrella, and offers an alternate explanation of the Gemara (not like Rashi) in order to avoid the question. However, his interpretation has its own sore points in my humble opinion, which is probably why Rashi rejected it.
Actually, the TOSFOS SHANZ citing the RIVA, printed in the Tosfos ha'Rosh on this Daf, raised this question well before the Sefas Emes. As he asks, isn't it clear that one is Chayav for carrying a bed to Reshus ha'Rabim in order to place a Mes on it?
However, he concludes that indeed Rebbi Shimon would classify an act such as being Motzi a bed for a Mes (or an umbrella for rain) as a Melachah she'Einah Tzericha l'Gufa, since this is not the type of Hotza'ah that was done in the Mishkan.
Regarding your point about weeding weeds, you are correct that the Gemara (103a) considers weeding one's field to be a Melachah she'Tzericha l'Gufa. However, your question on that Gemara does not hinge on the words of the Rashi in our Sugya (who is Mechadesh that Hotza'ah of an object that will be used for protection from something unwanted is Einah Tzericha l'Gufa, even though the object that one was Motzi is in itself a wanted object). You are asking a general question on Rashi's oft-reiterated opinion that anything done to undo a previous act is Einah Tzericha l'Gufa (- for example, see Rashi 93b DH v'Rebbi Shimon). Why isn't weeding considered an act done to undo the introduction of the weeds to the field, like Hotza'as ha'Mes?
It would seem that weeding is not simply the removal of unwanted growths. It also makes the soil more arable than it originally was, by loosening up the dirt etc. Thus, it is an act that has its own benefits and it is not just done to undo a previous act. This is, in fact, why weeding is classified as "Choresh" mid'Oraisa.
Best wishes,
M. KORNFELD