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In audiophile communities you often see a crazy amount of tweaking and gear designed around sound, but I'm curious on a technical level, are there known reasons why speakers don't sound as good as a real instrument? Or is a matter of time / money to make the difference indistinguishable?

I've heard things such as, size of the speaker, quality of the source recording, are there other things, or anything that prevents this from being possible?

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I have a Leslie speaker that wants to talk to you about the qualities of a Hammond organ with and without the Leslie. Also a number of electric guitar speakers insisting on their instruments being less than fabulous without their support.

Now getting back to the original question, it would appear that it's not as much speakers which are the problem but speakers employed for the sake of reproducing rather than producing sound.

Now the problem of reproduction is an entirely different one: speakers are supposed to be faithful rather than wonderful then, and you have a significantly lower number of speakers than original sound sources. Then it's easy to overlook that our problem does not just involve speakers: it involves imaging the original sound using microphones and mixes into few channels in the first place.

Now the speakers have to be neutral and universal, capable of reproducing everything without adding any oscillations of their own. That requires dampening them so that they don't ring on in any manner on any frequency. This dampening also affects their initial response (in particular, transient response) and their effectivity. Now transient response is a lot about phase coherence and humans specialize on on tiny discrepancies to provide spatial hearing in connection with irregularly shaped ears and tiny movements of the head and compensating for naturally occuring reverbation.

Reproduction speakers sit in an uncomfortable position between reproducing acoustics and producing acoustics: after all, you don't listen in acoustically dead rooms but add the acoustics of your present room to the mix, and both ears get signals from all speakers (closed headphones excluded).

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This isn't really going to be an answer, but an opinionated comparison. A hint towards an answer will be at the end...

The 'audiophile communities' have an odd sense of what sounds 'right'. They get caught up in minutiae which would be of no concern to a sound engineer.
They often end up with systems that are as far from 'true' as a cheap one put together with no thought. It may sound 'sweeter' but no more accurate.

Some of them spend so much time & effort listening to the 'sound' that they forget to listen to the music.

I've had the dubious pleasure of being round at someone's house when they just bought some new component & forced me to "listen how it handles this bit, with the horns... & the strings... & oooh, that cymbal" etc.

My studio monitors are better.

They're flatter, they don't emphasise anything, they just tell it how it is.
If I mix on there, the audiophile will love the result - because they can 'hear bits I didn't even know were there'... which is, of course, not true. I knew they were there, I put them there.

So, down to a hint at an actual answer.
People don't actually expect things to sound like they would if they were played in the room with them. They expect them to sound like they were recorded in a good, well-tuned room, with a microphone.
That, to most people, is actually what they think an instrument sounds like.
If you put it in the room with them, their brain would unconsciously filter out all the room acoustic & they would think all they can hear is the instrument. If you recorded that & played it back to them, they would suddenly change their mind... from a recording, your brain cannot do that job of removing the extraneous information - so the room sound becomes an irritation you cannot avoid.

When recording, you go to great pains to balance the room sound against the instrument, so that when the listener hears it, they don't have to try to extract one from the other, they're just given it sounding 'right'.
Additionally, all the odd frequencies that can add & subtract in a real situation must be evened out. You can do this either by brute-force, with Equalisation, or by careful selection & placement of the microphone[s] used to capture the sound.

The idea is that the listener is never consciously aware that this was done.
You do all this using studio monitors, that the average audiophile wouldn't even consider listening to, because they don't make things sound 'nice', they make things sound 'accurate'.

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I feel like this needs a lengthy answer but I'll try to give my short opinion.

First, when an instrument is played it creates a unique set of frequencies and overtones known as the timbre.

We know that human hearing ranges from 20Hz to 20kHz. With that knowledge most microphones and speakers are built to only respond within that range. (Some less and some a little higher)

We also know that frequencies affect each other and contribute to the overall tonal sound and quality see: here

There is also speculation that instruments produce frequencies above 20kHz (ultrasonic) and those frequencies affect (possibly) what we can hear. See: this study

So, I would argue that because most audio equipment, even in professional audio, seeks to only capture and produce sonic frequencies a microphone/speaker system does not produce those higher frequencies that produce the true richness and beautiful tone of a genuine Stradivarius. This is my own theory on this topic.

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