The gemara explains that the first two parshiyos that were read by the kohen gadol, since they were in close proximity to one another, it can be rolled from achrei mos to emor. But the third parsha which was in parshas Pinchos could not be rolled to and therefore he must read it by heart. The gemara explains that rolling wasn't an option because it was a lack of kavod tzibbur, as rashi explains, having everyone sit silently until they reach the spot. The gemara explains that although generally we take out multiple sifrei torah, that is only when each sefer torah is read from by a different person so that there was no insult to the original sefer torah and no issue of causing an extra bracha (since each person is going to anyway make their own bracha), but this was not an option for the Kohein Gadol's reading (it would be a problem of p'gam and causing an unnecessary bracha).
The Tosafos Yeshanim points out that although reading by heart is not a perfect solution because it is a violation of reading the written torah orally, it is the lesser of the two evils. The Tosafos Yeshanim (in first answer) understands that the issue of reading written Torah by heart is only a מצוה מן המובחר, and is therefore trumped by kavod tzibbur.
It would seem from the gemara that on a shabbos rosh chodesh where we need to read from two separate places, we take out two sifrei torah rather than roll. If there is only one sefer Torah, it would be better for one to read the second section by heart rather than rolling the Torah and causing the tzibbur to wait. However, this is clearly not the minhag.
The Beis Yosef (144) writes that the hagahos mordechai and Ritva both say that it is better to disregard the kavod tzibbur, rather than disregard the takanas chachamim to read the inyana d'yoma of rosh chodesh (or 4 parshiyos). It is unclear how they would work this into the gemara which seems to say the opposite. Perhaps they would say that in the time of the gemara it wasn't set as an absolute takana to read the korbanos of mussaf from a sefer torah, but once it has become the overwhelming custom, it is like a takanas chachamim that overrides kavod hatzibbur.
The Rashba in a teshuva cited in the beis yosef was asked about the possibility of reading the second section from a chumash when there is only one sefer torah, rather than rolling. The Rashba answers and proves from our gemara that it is better to read from a chumash rather than roll, because even reading by heart is better than rolling. Clearly, the Rashba holds that reading from a chumash which avoids both the kavod tzibbur problem and the issue of reading the written torah by heart, is the best solution.
Yet, the Shulchan Aruch paskens like the Ritva that we roll rather than read from a chumash, and the Darkei Moshe agrees. The Magen Avrohom (7) asks this question on the Shulchan Aruch, that the gemara itself says that even if there is no alternative but to read by heart, we prefer that to the rolling of the Torah b'tzibbur. How does the pesak of the Shulchan Aruch fit with the gemara (The Magen Avrohom is apparently not content with saying that it only developed into a "takana" to read that section b'tzibbur, after the time of the gemara)? The Magen Avrohom writes that the concern of Kavod Tzibbur was only in the large group that was in the ezras nashim to hear the Kohein Gadol read from the Torah, it doesn't apply to the small groups in shul because מסתמא מוחלין על כבודם כדי לקיים קריאת המפטיר דשבת ור"ח ומפטיר דיו"ט דהוא תקנת הגאונים. The Magen Avrohom seems to hold that the takana alone wouldn't trump kavod tzibbur, but since there was a takana to read the inyana d'yoma from the sefer torah, we assume the tzibbur would be mochel on their honor.
The Nesiv Chaim (gilyon of shulchan aruch) explains the position of the hagahos mordechai. In the time of the gemara where the one getting the aliya read from the Torah it was impossible for the section to be read by heart because no one knew who would get that aliya (it was only possible for the kohen gadol who knew that he would be reading it to memorize it in advance). Since that was not a solution, the custom became to roll the torah b'tzibbur, which carries over into nowadays when there is a ba'al korei who can technically prepare it in advance since we also have a shortage of people who can read it by heart. Being that it became impossible to sustain the reading of the parsha by heart, the tzibbur is mochel on their kavod to allow the rolling. The difficulty with this approach is that it can still be read from chumashim as the Rashba suggests.
The Pri Chadash actually writes that the Shulchan Aruch following the Ritva and Hagahos Mordechai on only allowing the rolling since we can assume the tzibbur is mochel. They are not suggesting that it is a better solution to just reading from a chumash. Therefore he writes that if they want to read from a chumash rather than rolling the sefer torah, they can certainly do that.
A simple answer would have been that reading from a chumash is more of a lack of kavod tzibbur than rolling, therefore we roll rather than read from a chumash. The Pri Megadim rejects this answer because the reading from a chumash is only a lack of kavod tzibbur because they don't have a Torah (so we don't allow them to read from a chumash to make them feel bad and purchase a Torah - Beis Yosef 143), but in this case where there is a sefer torah, there is no lack of kavod tzibbur to allow the second reading to be done from a chumash.