Why don't people use 專名號 to avoid ambiguity?
Proper name marks have largely fallen into disuse. That is because typesetting is difficult (as evidenced by your question) and that the text marked is usually understood by context.

我們有時看見一些書籍、文章中，已不使用專名號。這是因為印刷時比較困難，在約定俗成的情況下，現在已多不使用，並非錯誤所致。(古今標點趣聞)


Your concern for clarity is valid. But using proper name marks may cause further confusion in the case of eponyms. A Golgi apparatus does not carry any material attribute of its discoverer. Logically, it is just an organelle that just so happens to be discovered by Golgi. We all have Golgi apparatuses – what does Golgi (the person) have to do materially with our Golgi apparatuses? That is also probably why certain eponyms are no longer capitalised in English: e.g., abelian, newtonian, quixotic etc. Therefore, if you indiscriminately underline 高爾基, it may appear to some people that you are implying the apparatus belongs to Golgi (linguistically, attributive instead of genitive), much like 高爾基的帽子 (Golgi's hat).

I believe using parentheses also achieves clarity and is much more convenient (and commonplace) than using proper name marks.

大多數真核細胞有高爾基體（Golgi apparatus）。
范德華力（van der Waals force）是一種電性引力，但它比化學鍵或共價鍵弱得多。


I however agree that proper name marks may be useful in the context of classical Chinese, especially when annotating names of people and states. We may not have enough historical knowledge to parse the sentence correctly. For example, you need to be very familiar with the given name of Confucius (丘) to parse the following without the help of proper name marks:

孔子曰：「大道之行也，與三代之英，丘未之逮也，而有志焉。」《禮記》