Romaji is somewhat of a conversion from kanji and kana to the Roman alphabet.
What are the disadvantages of learning only or mostly romaji aside from being unable to read/write in kanji? I don't think there are many advantages.
Your question body contradicts the title, so I'll answer both questions:
Advantages of roomaji (I never thought I'd say this!):
Disadvantages of roomaji:
The real question is "Advantages/disadvantages for whom?".
For students of Japanese, Romaji is really useful when they start out, because they don't have to learn anything to be able to read it (although without learning Kana, they'll probably end up reading it incorrectly, especially if they're native English speakers :(). Another advantage is that Romaji text (unlike normal Japanese text) has spaces, which can really help the beginning student recognize word boundaries. Another minor advantage is that Romaji (especially Nihon-shiki or Kunrei-shiki, which is not so common in western Japanese teaching materials nowadays) sometimes makes it somewhat easier to catch verb conjugations where the stem-final consonant remains the same but the vowel changes (e.g.
These advantages make usage of Romaji acceptable for beginners, but there are disadvantages that make it a terrible burden for students who want to progress beyond that level. Most of them have already been described by Matti, so I wouldn't repeat them.
Japanese speakers are the second audience for Romaji usage, and they are often ignored in such debates. Most of the advantages and disadvatages for learners of Japanese don't apply to them, since they can already perfectly read and write kanji and kana. The reasons they would choose to use Romaji (as they, indeed, do quite often) is different:
Writing in Japanese when when using mediums that don't support Japanese text (such as computer software that has no Japanese support).
For typographic effect. This use of Romaji is incredibly common in advertisements and in logos.
For typing Japanese on the computer. Japanese keyboards have kana, and you can certainly set it to kana-mode use the kana keys for input, but from my experience, most Japanese actually prefer to input Japanese in Romaji-mode instead.
By transcribing everything into latin alphabet (heck, even to hiragana/katakana syllables), written Japanese will lose most of the legibility than if it were to be written in full kanji+kana. It may be hard to describe, but let me give you a nonsense english sentence:
Wheel you go two the par tea two knight at ate? Eye think it's awed they are having it so far aweigh. Eye wont to reed this book, have you red it? Herald was in this mourning's gnus. Eye bet heal be surprised to here that.
The above is what Matti was saying in his third point about homophones/homonyms.
Not only that, by not using kanji, you lose the ability to instantly make out what is being said in a text, something that is very essential in speed reading (which is also why I have a hard time playing those FamiCom games; they lack kanji for the most part).
I've softened significantly from my beginner-level "all romaji should be purged from the earth" fanaticism. There are two related questions here, "Should I avoid a roomaji-based textbook like the plague?" and "Can I get away with learning Japanese without studying kanji?"
The TLDR version is "No" and "Yes, but you obviously will be illiterate".
"Should I avoid a roomaji-based textbook like the plague?" - No, roomaji does have some significant advantages in some contexts
"Can I get away with learning Japanese without studying kanji?" - Sorta... but here's where you'll face issues
** Some have claimed that using roomaji somehow retards development of proper pronunciation. This is simply false, and I have to question if those adhering to this idea have ever studied a western language. Does "ll" or "j" in Spanish cause anyone any trouble after the first 2 weeks?
I personally think there are no advantages to using romaji whatsoever. I think it's just a crutch beginners use to not have to memorize them, but it should be something you embrace. Hiragana and Katakana do not take that long to learn (assuming you have the motivation). Once you can read and write them well, it's almost hard to go back to reading/writing romaji. From there, you go on to kanji. It's also difficult to go back to using pure kana once you're comfortable with kanji.
I think learners should try to spend 99% of their time using the Japanese writing system and not romanization:
Reading is a highly overlearned skill, and it takes absolutely huge amounts of practice to become literate in the Japanese writing system. Since learners have limited amounts of time, it's to their advantage to start using kana and kanji as early as possible.
The flip side of point 1 is that if you practice reading romanized Japanese, you'll get better at it. That might not sound like a disadvantage, but it is! When rōmaji seems easier than kana and kanji, some students develop bad habits like mentally converting, or even converting on paper! And this can be a major problem for some students who never manage to move beyond rōmaji.
There usually isn't a one-to-one correspondence between the two. Very rarely is romanization a transliteration of kana and kanji as you claim; instead, most systems of romanization are designed as transcriptions of speech. Generally speaking that's helpful, but it unfortunately means you'll have to relearn the spelling of a number of words when you switch, and relearning has a high cost.
For example, in one common system 王(おう) is ō while 追う is ou. On the one hand it's helpful because unlike kana it represents pronunciation, but on the other hand it forces you to relearn down the road, which is unfortunate.
So I definitely would not recommend romanization for learners in general.
There are advantages to romanizing! And as long as you spend 99% of your time using kana and kanji, it shouldn't hurt to romanize when it's to your advantage to do so. Most of these advantages are related to pronunciation or to being able to divide kana into CV pairs:
The biggest advantage is that it's much easier to discuss morphology using rōmaji. Why? Well, see this post by Alexander Vovin for some discussion of how morpheme boundaries don't always line up with syllable boundaries. Kana forces you to segment things in an artificial manner that doesn't quite match the Japanese language itself―note that most Japanese verb stems actually end on consonants and not vowels!
Phonemic romanization is very helpful for discussing phonology without worrying about kana boundaries. For example, we could talk about the historic /au/ → /oo/ sound change in 書かう→書こう, or we could talk about /ai/ → /ee/ in じゃない→じゃねえ, or the assimilation of /rn/ -> /ɴn/ in 分からない→分かんない, and so on.
It can also be useful to romanize older forms of the language, as in the Oxford Corpus of Old Japanese (OCOJ). Kana were not always pronounced the way they are now, and romanizing can prevent the reader from making certain false assumptions about sound-character correspondences.
Romanization is also helpful for communicating with linguists or others who are unfamiliar with the language and can't read kana or kanji themselves.
You've probably noticed these are all related to linguistics, and I don't think that they're things beginners need to worry about. Personally, I'd say you should learn to read kana and kanji first. Worry about this stuff down the road, after you're already comfortable reading Japanese as it's normally written.
The disadvantages are all in the corner cases. Some romanizations represent づ and ぢ as "zu" and "ji" respectively, which is less than perfectly accurate since those are also used to represent ず and じ (I represent them as "dzu" and "dji" myself, but one can't force others to do so). And that's not even touching upon the issues with katakana and strange combinations such as ウィ and the like.