I'm talking about names like Livy, Plutarch, Aristotle or Virgil. What's wrong with Livius, Plutarchos, Aristoteles or Vergilius? Obviously they would still be pronounced completely differently, but that is true of the former set as well, and at least in the written form they are more faithful to the original names.
I should mention that I'm Czech, and sure enough, we also use different names for certain historical figures, such as Ježíš, where English speakers would use Jesus. We also often change names of foreign royalty if the name has a Czech equivalent (we still do that, such as queen Alžběta II for the current ruler of the UK), but again this is also done in English with Peter the Great, Frederick the Great and so on.
But the mentioned names seem a different case. Surely they are not equivalent English names, and it certainly can't be done to capture the pronunciation better, because let's face it, normal English pronunciation is completely incapable of doing the names any justice either way. So what gives? Why change them at all?
And while I'm on the topic of English pronuciation, is there any serious movement in English-speaking academia towards more faithful representation of names of historical figures or places, or is this seen as pointless (or do they do that already, perhaps)? It seems to me that English has truly given up on this. For example, on the wiki pages for Tiberius or Plutarch or Plato, pronunciation guides are shown next to the names. Except they are completely wrong. They simply assume the names were written in order to be read in English. I'm currently listening to the History of Rome podcast and enjoying it, but holy hell, it is irritating to listen to those mangled names. It's all Tie-beerius, Feybius, Jermennicus or Neerow. There's also a point where the author is corrected on the pronunciation of Cannae, and goes from saying Ca-NAY to Kenni. Which isn't really much of an improvement.
And I know that I'll probably just have to deal with it, but is this something to be expected for decades or centuries to come, what with the English dominance on the international stage?
I'm not sure I understand this question. You acknowledge that all languages, over time, alter some names to be more in line with that language's linguistic conventions. Neither English or Czech calls Jesus "Yeshua" or "Iesous", if we prefer to go back to the Greek rather than Hebrew. Why would it be any different for Titus Livius or Vergilius Maro? To the French, Livius is Tite Live. To the Italians, he's Tito Livio. Why is English a special case here for you?
I'm also puzzled by the assumption that this is a choice that one person (or a group of people) made to change the names of figures from ancient history, rather than developments over time. Shakespeare called it "Antony and Cleopatra" rather than "Antonius and Cleopatra" because that was how the people of his time referred to Marcus Antonius. Asking this question feels like asking why the French changed the Latin word "caballus" to "cheval"; it wasn't a conscious choice.
As for Wikipedia pages... The pronunciation guide on a Wikipedia page is meant to help you pronounce the word in the language it's in, not the original language the word derived from. As far as I know, every language's wikipedia is like this.
In academia, some scholars do prefer to stick the original spellings (or close transliterations of original spellings for Greek). But most don't out of convenience or to make the work more readable to a modern audience. Both, I think, are acceptable choices. If a scholar chooses the latter... Well, it's the same reason nobody in English will pronounce Caesar "Kaisar," even if that's closer to how it would be pronounced in Latin; to an English speaking audience, most people would assume you're talking in German. And sure, there can be mispronunciations that are irritating (Kenni?), but language isn't a static thing, and people inexperienced with the names will have trouble figuring out "proper pronunciations," in any language.
It's not just an English thing; other languages have long done the same thing. The French have their own versions for Greek and Roman names, as do the the Spanish. It helps make the names easier to pronounce in the language. For instance, Platon is more natural in French than Plato. Similarly, in Spanish they say Platón. Ulysse (French) and Ulises (Spanish) work better than Ulysses. Even Ulysses is a change from the Greek Odysseus. I'm sure there are other examples for languages I do not know.
The traditional English pronunciation of Latin follows its own rules, which map developments in English over the centuries.
Pretty much all European languages do something similar: listen to the same Latin name in Fremch, German, and Italian, and you will almost always notice striking differences.
Follow up, why do Greek names occasionally get different spellings in English when it doesn't change the pronunciation at all? I often see Comnenus replaced for Komnenos--since C and K are pronounced the same, and there is no C equivalent in the Greek alphabet, why use it? Is there some standardized rule for romanizing Greek which includes replacing K's with C's?
They conjugated proper names in Latin. So the endings don't really matter. So when searching something like Perseus for all usages of a name it's better to have an established go database in there that all conjugations of Divius Julius return to a single set. Hell just trying to ignore Macrons like every single Latin teacher does after the first semester is a godsend. It's better to use an already established tradition of spelling for academic purposes anyway, because if you've ever tried to do research on Ancient Asian names the fun of guessing which spelling was used is a blast. Especially ones that never made it into a Wade-Giles or Pinyin lexicon. I have no idea how it was even attempted before search operators other than blind luck of scanning through every article ever written and wondering if this inscription Tchindus is Genghis or not.