I've asked a number of native Chinese speakers if they think that they should scrap the current writing system in favour of pinyin or zhuyin fuhao ("Chinese romaji" and "Chinese kana," respectively), and the best argument against it that I've heard so far is that of the limitation of expressiveness in writing. This person did not argue that spoken language cannot be properly expressed in pinyin, but that the current written language cannot be.
Due to the nature of Chinese characters, a writer wanting to be concise may remove significant portions of a sentence, chop words in half, or rearrange everything in such a way that it would not be understood in speech. There are also many common words and phrases -- particularly four-character idioms -- that are popular in writing, but, again, incomprehensible if spoken. A writer may also engage in wordplay, using alternate characters that give a different "feel" to a word or change the emotional "tone of voice" (which was the one part of speech that he felt would be hard to express in pinyin), or replacing them with characters for another, similar-sounding word. He may purposely use characters with ambiguous meanings or pronunciations, or ones that are very precise. He may represent the speech of a man from Taiwan in traditional characters, that of a woman from China in simplified, that of a child in zhuyin fuhao and that of a man from Canada in pinyin (I've seen similar things in Japanese, using hiragana for children and katakana for foreigners, for example). By limiting writing to only pinyin, that literary tradition will be lost, and writers will be significantly limited in the ways in which they can express themselves.
He likened it to the use of acronyms and emoticons on the internet. If one day our ability to use things like "LOL" ":'(" "(>^_^)>" "<3" or " B)" were taken away because such things do not exist in speech and thus have no place in writing, then our ability to express emotions would be limited, and we would have to find new, possibly less-satisfactory ways to express ourselves:
"..and then he told me it was over. I am making a sad face and am crying."
"Don't worry, you'll find someone better. I am smiling and giving you a hug. I am expressing my care for you in a way that one might represent by drawing a picture of a heart, or of two people embracing each other."
"Thank you. I am smiling now."
I don't really think the benefits of literary expressiveness and conciseness outweigh the benefits of scrapping Chinese characters, but it's the most compelling argument I've heard so far.