負う and 王 are both hepburn-romanized as ou though. 方 and 頬 (hou vs hoo) is a better example. I don't really think native speakers still distinguish these.
Feel free to try listening yourself though:
頬, note that it has multiple pronunciations but we only care about hoo: https://forvo.com/word/%E9%A0%AC/#ja
方 https://forvo.com/word/%E6%96%B9%E3%80%80%EF%BC%88%E3%81%BB%...
In some cases though there is still a clear difference in pronunciation for most speakers, ex 塔 vs 遠
Could you elaborate on the last sentence? Wiktionary claims they're pronounced the same modulo pitch accent, but Wiktionary's phonetic transcriptions are (mostly?) auto-generated AFAIK.
> 負う and 王 are both hepburn-romanized as ou though
No, it's ou vs ō.
Nope! Writing 王 as "ou" is "wāpuro rōmaji" or modified Hepburn. Proper Hepburn wants ō. Which cannot be used for 負う.
> 方 and 頬 (hou vs hoo) is a better example.
As a native Japanese speaker, this example is eye-opening. I hadn't even realized that the u in 方 is pronounced as /o:/ — I believe most Japanese people haven't either, despite unknowingly pronounce it that way.
Also, I have no idea how to Hepburn-romanize 方 vs 頬, 負う vs 王, and 塔 vs 遠. If I had to romanize, I would just write it as whatever the romaji input method understands correctly (hou/hoo, ou/ou, and tou/too, in this case).