In my opinion, only the reverse could be true, i.e. that Unicode does not need pre-composed characters because everything can be written with composing characters.
The pre-composed characters are necessary only for backwards compatibility.
It is completely unrealistic to expect that Unicode will ever provide all the pre-composed characters that have ever been used in the past or which will ever be desired in the future.
There are pre-composed characters that do not exist in Unicode because they have been very seldom used. Some of them may even be unused in any language right now, but they have been used in some languages in the past, e.g. in the 19th century, but then they have been replaced by orthographic reforms. Nevertheless, when you digitize and OCR some old book, you may want to keep its text as it was written originally, so you want the missing composed characters.
Another case that I have encountered where I needed composed characters not existing in Unicode was when choosing a more consistent transliteration for languages that do not use the Latin alphabet. Many such languages use quite bad transliteration systems, precisely because whoever designed them has attempted to use only whatever restricted character set was available at that time. By choosing appropriate composing characters it is possible to design improved transliterations.
> It is completely unrealistic to expect that Unicode will ever provide all the pre-composed characters that have ever been used in the past or which will ever be desired in the future.
I agree it's unlikely this will ever happen, but as far as I know there aren't really any serious technical barriers, and from purely a technical point of view it could be done if there was a desire to do so. There are plenty of rarely used codepoints in Unicode already, and while adding more is certainly an inconvenience, the status quo is also inconvenient, which is why we have one of those "wow, I just discovered Unicode normalisation!" (and variants thereof) posts on the front-page here every few months.
Your last paragraph can be summarize as "it makes it easier to innovate with new diacritics". This is actually an interesting point – in the past anyone could "just" write a new character and it may or may not get any uptake, just as anyone can "just" coin a new word. I've bemoaned this inability to innovate before. That is not inherent to Unicode but computerized alphabets in general, and I that composing characters alleviates at least some of that is probably the best reason I've heard for favouring compose characters.
I'm actually also okay with just using composing characters and deprecating the pre-composed forms. Overall I feel that pre-composed is probably better, partly because that's what most text currently uses and partly because it's simpler, but that's the lesser issue – the more important one that it would be nice to move towards "one obviously canonical" form that everything uses.
There is also another reason that makes the composing characters very convenient right now.
Many of the existing typefaces, even some that are quite expensive, do not contain all the pre-composed characters defined by Unicode, especially when those characters have been added in more recent Unicode versions or when they are used only in languages that are not Western European.
The missing characters can be synthesized with composing characters. The alternatives, which are to use a font editor to add characters to the typeface or to buy another more complete and more expensive version of the typeface, are not acceptable or even possible for most users.
Therefore the fact that Unicode has defined composing characters is quite useful in such cases.
Every avenue opens inconveniences for someone, but I'd rather choose the relatively rare inconvenience of font designers over the relatively common inconvenience of every piece of software ever written. Especially because this can be automated in font design tools, or even font formats itself.
The pre-composed characters are necessary only for backwards compatibility.
It is completely unrealistic to expect that Unicode will ever provide all the pre-composed characters that have ever been used in the past or which will ever be desired in the future.
There are pre-composed characters that do not exist in Unicode because they have been very seldom used. Some of them may even be unused in any language right now, but they have been used in some languages in the past, e.g. in the 19th century, but then they have been replaced by orthographic reforms. Nevertheless, when you digitize and OCR some old book, you may want to keep its text as it was written originally, so you want the missing composed characters.
Another case that I have encountered where I needed composed characters not existing in Unicode was when choosing a more consistent transliteration for languages that do not use the Latin alphabet. Many such languages use quite bad transliteration systems, precisely because whoever designed them has attempted to use only whatever restricted character set was available at that time. By choosing appropriate composing characters it is possible to design improved transliterations.