I can’t remember the source (please let me know), but I’ve heard that the reason why there are doubles of a negative and positive mitzvah for doing or not doing the same action is that Hashem wants to add to our Schar, but I don’t understand how that works. Let’s take the example of Tzidaka. There’s a positive Mitzvah to give and a negative mitzvah to not withhold. If you give, you get reward for the positive Mitzvah. If you withhold, you get punished for violating the negative and you also get punished for the Bitul Ahsay. So it seems like it can only work against you? (other examples are chilul Hashem/kiddush Hashem, and listen to the Gedolim/lo Tasur)
There is a verse in Kohelet (7:14) which states "zeh le'umat zeh asah Elokim", meaning that G-d made things and their opposites or counterparts. Rashi there explains that G-d made the good and its reward and the bad and its compensation. Chazal in many places (See Vayikra Rabba 34, Psikta D'rav Kahana 28) made this verse into a concept saying that G-d made the rich and the poor so that they both benefit each other; the rich giving the poor and the poor, though not by will, creating the opportunity for the rich to benefit them. In addition, Chazal, also in many places (See for example Baba Metzia 70b) have the concept that the Torah added a positive mitzvah to an already existing negative mitzvah. Though as you correctly said there is the downside of transgressing two mitzvoth at once and being punished for it, there is the upside of getting rewarded for the abstaining from sin and in addition getting rewarded for fulfilling a mitzvah.