Using the exact pronunciation is often difficult between languages because certain sounds in English don't exist in other languages and vice versa. A common example is the "trilled r" in Spanish. In the opposite direction, Japanese doesn't make a distinction between r and l, as it exists in English. Others have tones or use unique sounds like the click consonant. It's much easier to make an approximation of the original word rather than use the exact pronunciation.

Then there's historical context. Germany is derived from what the Romans called the area (which they likely adopted from the Guals), while Germans call themselves the Deutsche, which is derived from the Old German word for "the people." We could start calling them the Deutsche as well, but after hundreds of years of calling them the Germans, there's just not much point in changing it.

And if you change one, you're going to have to change China into Zhongguo, Japan into Nippon or Nihon, Korea into Hanguk, Greece into Elliniki, Egypt into Misr or Masr, Hungary into Magyarorszag, Finland into Suomi, and so on. And that's just country names. Similar examples can be found with names for cities, regions, rivers, etc.

So, it's just easy to keep using the accepted terms in English.