Well, they have the advantage that people will typically understand what word was meant even if using only Latin letters, with a bit of context. If they had been entirely different unrelated glyphs, it may be much harder to understand in situations in which you are limited to the Latin alphabet.

Of course, it's debatable whether diacritics were a better solution than using letter combinations. There are some canonical replacements already - sh for ș and tz for ț - and some could have been created for the extra vowels. This is especially puzzling since we already use letter combinations instead of diacritics for the Ç sound (c-e/i) and the soft G sound (g-e/i).