Answer

Nowadays, unfortunately, we do not abolish anything. But the source you cited deals with a different case: if an enactment has already been abolished, can it be reinstated (or is authority required to enact it מחדש). That is a different question. On the contrary, it says exactly that it cannot be abolished, because there is no authority to do so. However, once people already abolished it (whether with authority or without authority), a custom was created, and now the question is whether one is obligated to preserve it. One must remember that every custom is a breach of a halakhic boundary (whether toward leniency or stringency), and the obligation to preserve a custom is an obligation to preserve that breach of the boundary. As for the ignorance, some claimed that this was not only an enactment for those who do not know how to read, but that the repetition turns the prayer into a public prayer. But that is a post facto explanation.
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Questioner:
Following up on my question about abolishing the repetition of the Amidah, see the email below, which says that in some yeshivot they abolished the repetition of the Amidah at the afternoon prayer. Can this be relied on in order to abolish the repetition of the Amidah in regular synagogues as well?

Question: Sometimes, instead of the usual practice for the afternoon prayer (where after Ashrei the congregation recites the Amidah silently and afterward the prayer leader begins the repetition of the Amidah), they do a “short Mincha” (that is, immediately after Ashrei the prayer leader begins the Amidah out loud, up to “Kedushah” and “the holy God,” and then everyone prays silently, and afterward there is no repetition of the Amidah again). According to Jewish law, when may this be done, and why do yeshivot do this as a matter of routine?

The short answer: a shortened prayer as described is intended only for pressing circumstances, such as when one fears that the time for prayer will pass, etc. As for the fact that yeshivot have adopted this as standard practice, some have indeed objected to it, while others have justified the custom for various reasons, as explained below.

The fuller answer:

According to the Rema (Orach Chayim 124:2), one recites a shortened prayer only “in a pressing circumstance, such as when one fears that the time for prayer will pass” (that is, that the prayer leader will not manage to finish the eighteen blessings within the time for prayer—see the Mishnah Berurah there; and the Mishnah Berurah also adds that the same applies to the morning prayer if there is concern that the prayer leader’s prayer will not be completed within the time for the morning prayer). And the Mishnah Berurah emphasizes there in subsection 6: “Without a pressing circumstance, many of the later authorities agreed not to do this, because the primary enactment as a matter of law is to pray first silently and afterward out loud.”

[And some say that in a place where there is concern that during the repetition of the Amidah there will not be nine people listening and responding, they should also do it this way—see the booklet Tefillat Miriam in the book Shirat Miriam, siman 47 note 140.]

But if so, one must ask: why is it the routine custom in many yeshivot to pray a “short Mincha,” even when there is no pressing circumstance?

In the booklet Tefillat Miriam in the book Shirat Miriam, siman 47 note 140, the following is brought on this matter:

“As for the basic custom in several yeshivot to pray a short Mincha, it is explained in the book Emet LeYaakov (siman 124 note 152) in the name of Rabbi Yaakov Kaminetsky, that the reason is that the main enactment of the repetition of the Amidah was only in the synagogue, where the unlearned would pray and did not know how to pray, but in the study hall, where only Torah scholars prayed, they did not enact the repetition of the Amidah at all. Only in the morning prayer did they repeat the prayer even in the study hall, because of adjoining redemption to prayer, since they cannot interrupt after ‘Who redeemed Israel’ and listen to the prayer leader until Kedushah, and therefore they had to pray themselves and then return to hear the repetition of the Amidah.

I also heard from one sage, may he live long, that the reason for the custom in those yeshivot—on days when there is a general lecture, they pray a short Mincha—is that they feared that because of the heat of Torah study they would go on discussing the learning after the lecture at the expense of the afternoon prayer, and it is preferable that they talk while the prayer leader says the first blessings out loud rather than when the congregation begins the silent prayer.

And in fact many opposed this custom in some yeshivot, and see the book Pe’at Sadcha (p. 114), which quotes Rabbi Aharon Dushnitzer as having been distressed by it, though he did not abolish this practice even in his own place. And it is written there that in our time, when the deferred boundary has already been breached by this practice in some yeshivot, it is a commandment for whoever has the power to uproot this practice completely, so that it should neither be remembered nor revisited. However, see also the responsa Az Nidberu (vol. 12, siman 23) for what is written on this matter.”
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Rabbi:

That is not really abolition but abbreviation. Since the reason for the enactment no longer applies, I do not see why one should not cut corners as much as possible within the framework of Jewish law. So yes, one certainly can do this.
By the way, in my opinion the custom in yeshivot is simply because of neglect of Torah study.