I was able to locate only one reference discussing how public Torah reading was done (i.e. - who read it):
Originally the Torah was read in public once every 7 years during Hakhel
Mishneh Torah, Laws of Festival Offering (Chagigah)3:3 excerpt from Sefaria:
אֵימָתַי הָיוּ קוֹרִין. בְּמוֹצָאֵי יוֹם טוֹב הָרִאשׁוֹן שֶׁל חַג הַסֻּכּוֹת שֶׁהוּא תְּחִלַּת יְמֵי חֻלּוֹ שֶׁל מוֹעֵד שֶׁל שָׁנָה שְׁמִינִית. וְהַמֶּלֶךְ הוּא שֶׁיִּקְרָא בְּאָזְנֵיהֶם.
When would they read? At the end of the first-day holiday of the festival of Sukkot, which is the beginning of [the festival's] intermediate days, on the eight year [of the sabbatical cycle]. And the king would be the one to read in their ears,
Jerusalem Talmud Megillah 29a mentions that Ezra establish public reading on Mon., Thurs. and Shabbat Mincha. However, it does not mention there who read it or that there were aliyot. The only inference I could find is that in Ezra chapter 8, we see that Ezra, himself, did the public reading.
Mishnah Megillah ch 4:1 and 2 discuss the number of aliyot to be given on weekdays, Shabbat and other holidays.
Apparently, by the time the Mishnah was written, the concept of aliyot had already occurred.
When and why did this method change to giving aliyot? What purpose do these "aliyot" accomplish? I.e., if one person read it, what was "wrong" with it that the method was changed?