The Acharonim ask this question. It could be, based on the words of Rashi, that this Halachah applies only to a person who is the regular Haftarah reader. We honor him with the other privileges, in gratitude for taking upon himself the burden of being the regular reader of the Haftarah, or in order to prevent quarrels. But these privileges do not apply to someone who reads the Haftarah only on occasion, where one person sometimes has an Aliyah to read from the Torah, and the other to read from the Navi, and at other times vice versa. Since nowadays we do not have the practice to have the same person read the Haftarah each week, these privileges do not apply.

See also CHIDUSHEI HA'NETZIV for an entirely different approach (than Rashi's) to the Sugya; according to the Netziv's explanation, too, these Halachos do not apply nowadays.

See also what we wrote in YOSEF DA'AS.

Yosef Ben-Arza

The YOSEF DA'AS writes that since this practice applies only to a place where the custom is to have the same person read the Haftarah regularly each week, the Poskim omitted this practice because the custom to have the same person read the Haftarah each week no longer exists.

When the Rambam records Halachos that are not practiced today, that is because they will be practiced when the Beis ha'Mikdash is rebuilt (such as the Halachos of the Korbanos, Yovel, Arei Miklat, Dinei Nefashos, etc.). However, he does not record practices which were practiced only in a certain time and certain place and are no longer relevant because the custom no longer exists (unless that custom is dependant upon the presence of the Beis ha'Mikdash or on all of the Jews being in Eretz Yisrael, in which case he records the practice since it will, in the future, be relevant).

All the best,

Yisrael Shaw