First, it's worth noting that these are transcriptions, used by linguists, not actual orthographies used by native speakers. The ancient Sumerians didn't write their word for "god" as diĝir; they wrote it as 𒀭. And the people who spoke something like Proto-Indo-European never wrote it down at all. It's only modern scholars who use the Latin alphabet for this.
And since these are modern transcriptions of extinct or reconstructed languages, we generally aren't sure how the sounds were pronounced! Some scholars think that Sumerian ř was pronounced like IPA
/t͡sʰ/, but others disagree, and some argue that it wasn't a distinct phoneme at all (just an artifact of a sound change in progress).
All that we can be certain of is that certain words (like guř "ox") are sometimes transcribed with Akkadian phonetic signs containing
/d/, and sometimes with Akkadian phonetic signs containing
/r/. So if you want to talk about this new maybe-phoneme without getting into the weeds of how it was actually pronounced, ř or dr are reasonable names to pick.
Or, sometimes it's for reasons of typesetting (like Sumerian ĝ being much easier to type than ŋ until very recently), or to show that something is a single segment (PIE *kʷ is generally considered a single phoneme, rather than *k followed by *w). In the end, these transcriptions are mostly only used by specialists in specific fields, who quickly get used to all the idiosyncracies. With no native speakers using these transcriptions in day-to-day life, practicality isn't much of a concern.