There's a few reasons, and they are interrelated.

Let's go with the Latin examples for the moment. We don't speak classical Latin, well not most of the time anyway, so we tend to anglicise names. Some of those names have a long history of being anglicised in a particular way. So everybody just says 'Tacitus' with the c as an s sound. This fits English pronunciation and orthography patterns. Most classical names have this kind of history. It's even stronger when you consider that classical Greek names are usually anglicised through a Latinate version.

Secondly, deliberately pronouncing foreign words with a foreign intonation and accent tends to sound like one of two things. Firstly, say we were discussing Tacitus and conversing in English, and I made a deliberate point of pronouncing the c as a k, and getting vowel length and accent correct for the name as it would be in Latin. Either (a) I'm drawing attention to the word as a foreign word. It's like I went out of my way to use a french pronunciation of différance to highlight that I meant it in a technical, Derrida-related sense. Or (b) I'm just being pretentious and showing of my knowledge of Latin.

Thirdly, while Tacitus seems like a word we could get right, not all languages anglicise so easily. Чингис Хаан is regularly butchered in English pronunciation. 'Chingis Khan' is a reasonable approximation, but getting both the /kh/ sound and the /ng/ sound in Хаан right is fairly rare. And let's not even get started on Genghis. But Genghis is common and accepted, because (a) usage trumps 'rightness', (b) the mapping of Mongolian to English sounds is not straightforward, and approximation is inevitable, (c) going around making a point of saying Чингис Хаан just sounds pretentious to most people.

In addition to the good answer above, all languages tend to "round off" pronunciation to fit their tongues. Excellent example is to look at words the Welsh borrowed from English ("toilets" becomes "toiledau"). Same thing happens from Latin to any other language, especially since us Westerners almost always inherit our pronunciation from medieval pronunciation. Go to a GregorIan chant group, and one of the first things the instructor will ask is whether you use Italian or Central European accent in your Latin, because the change was already happening by then.