There are arguments in the Rishonim about what the 613 mitzvos are. But even if you hold something's not part of the 613, it's still a mitzva, so what's so special if it is part of the 613?
This is a very important question which bothered me for a long time by until I saw the explanation of Rav Yeruchom Perlow in his introduction to the commentary on the Sefer HaMitzvos of Rav Sa'adyah Gaon.
The question that he addresses is why some of the Gaonim and Early Rishonim invested so much time and effort in working out the list of the 613 mitzvos. He answered that since on the one hand Chazal teach in several places that there are 613 mitzvos, and on the other hand there are clearly many more mitzvos than this, a set of rules are needed in order to determine which mitzvos should be included in the list of 613. Each one of these early authorities had his own set of rules (the Rambam spells out clearly what his rules are) and thus they each end up with a different list.
And the importance of working out which mitzvos go into the list is this: there are many mitzvos mentioned in the gemara which are not clear if they are d'oraisa (from the Torah) or d'rabanan (from the Rabbis). Even when a mitzvah seems to be derived from a posuk sometimes it is only an asmachta (a mitzvah d'rabanan which is supported by the Torah, but which does not come from the Torah). But if the mitzvah is in the list of the 613, then it is most definitely d'oraisa. And if it is not in the list then the determination of whether a certain mitzvah is d'oraisa or d'rabanan has to be made some other way, or remains a doubt.
The sages teach that the 365 negative commandments parallel the 365 blood vessels and tendons (Gidim), and the 248 positive commandments parallel the 248 limbs (see shaarei kedusha and Mishnah in Ohalos 1:8 which lists them).
Hence, there is special significance to those included and special kavanos to have when fulfilling them as alluded to in shaarei kedusha part 1.
Therefore a man should seek out with all his strength to fulfill all the 613 commandments, and when he fulfills a positive commandment, he should have kavana (mental intent) to remove from that specific limb of his soul which corresponds to that mitzva the impurity of that klipa. And then the limb of that holy mitzva will settle on him after the impurity has been removed, as in "and their sins were on their bones" (Yechezkel 32:27). Because when this one rises, this one falls. And likewise when a sin comes one's way, he should refrain from doing it, and he should have kavana (intent) that through this the impurity in the specific gid (pipe) of the soul which corresponds to that sin shall be removed. And then he will be able to pass the spiritual energy which is drawn through the spiritual pipe, and through this his soul will be a chair and a chariot for His holiness, may He be blessed, and this is the Sod (secret meaning) of "the forefathers, they are the chariot" (Midrash Raba - Bereishis 47:6, Zohar 1 Daf 173)
Note the reason the Rambam actually gave in his hakdama (https://www.sefaria.org/Sefer_HaMitzvot%2C_Introductions%2C_The_Rambam's_Introduction?lang=bi): He needed a way to organize his Mishnah Torah, so he wanted to give the mitzvos relevant to each section (the "keser" to each book). Then he saw that others had different lists, so he had to explain and justify his list... Rav Yaakov Weinberg z"l once pointed this out to me. It really doesn't make this pursuit sound very important at all. Just sayin'.
Update: "why some of the Gaonim and Early Rishonim invested so much time and effort in working out the list of the 613 mitzvos." Worth noting that according to the Rambam, only the Behag "invested so much time and effort". The Rambam says in his hakdamah that other Rishonim mostly just took the Behag's list as a starting point and tweaked this point or that. Then others wrote piyutim about the subject, which the Rambam says is fine as music goes, but not that relevant in terms of really working it out correctly.
After the Rambam, of course, we all have an additional reason for studying it: The words of the Rambam, his explanations, the alternate point of view of the Ramban - all that became a subject in itself.