1. Once you start writing sentences, hiragana is no longer readable.
This is only because their are no spaces. Why not just make spaces? (Follows on to below Q)
2. Kanji gives meaning to words.
Yes this is true, but only because there are so many different words that sound identical, which is brought about by there being so few sounds you can make with the Japanese language.
3. It looks nicer when you write in kanji.
Yes, Kanji can be beautiful. But many people think it can look cluttered and messy. Beauty is in the eye of the beholder.
4. Kanji is easier to read.
Kanji would be easy to read, if you learnt, mastered, and read many times the particular Kanji you were reading at that time. But then again that's true of anything you learn, master and look at a lot.
5. Kanji Takes up less space.
This is a common misconception that I don't agree with at all. Complex Kanji can be very difficult to read, even for native speakers, when it is written in small font. Kanji written on A4 paper is generally as small as it can be, whilst Latin alphabets can go several fonts smaller whilst still being readable. Yes, Japanese is typically shorter than English in practice, but that's only because the Latin font isn't as small as what it could be.
6. It could be worse.
Well yeah I guess it could be. But then again it could be a lot easier too.

Don't get me wrong, Japanese as it stands today couldn't get by without Kanji. What I'm saying is that no language is perfect, and there are many inefficiencies with Japanese, in particular its reliance on Kanji, just like any other language.

I have been learning Japanese for 3 years now. As a native Chinese speaker, I have to say that personally I find Japanese much easier to read AND to understand when it's written with kanji. (Reason #1 as discussed.)

I think you can add another reason: kanji also facilitates cultural exchange and communication in the Sinosphere (漢字文化圏). For example, even in Korea, where usage of hanja (the Korean name for Chinese characters) is now very limited, they still use hanja together with their native hangul for signs to help tourists. For example, Chinese or Japanese tourists will understand with no problem a sign that says “出口” (“chukou” in Chinese, “deguchi” in Japanese), but they might not recognize what an “Exit” is. (Not everyone knows English, you know?)

A simple Chinese sentence: 我的弟弟去年買了一頭牛。

Even without any knowledge of Chinese, a Japanese speaker will somehow know that the sentence has to do with “I”, “younger brother”, “last year”, “buy”, “a cow”.

Japanese translation: 私の弟は去年牛を一頭買った。
“My younger brother bought a cow last year.”

See the similarities between the Chinese and the Japanese sentences?

This is why I think it's a shame that Korea virtually abandoned the use of hanja. If they had continued to write Korean in hanja-hangul mixed script, then it would have made communication a lot easier among the Chinese, the Japanese, and the Koreans today.

Here's a segment from the preamble of the Korean constitution:

Hangul only: 유구한 역사와 전통에 빛나는 우리 대한 국민은…
Hanja + Hangul: 悠久한 歷史와 傳統에 빛나는 우리 大韓國民은…
Japanese translation: 悠久の歴史と伝統に輝く我が大韓国民は…
Chinese translation: 擁有悠久歷史和光輝傳統的大韓國民…
English: We, the people of Korea, proud of a resplendent history and traditions dating from time immemorial…

Very interesting, don't you think?