Must speakers have certain volume to sound convincing ?

One hears with their brain not their ears. That was my point early on. We are all slaves to our experiences, education and preferences built over our lifetime.
Also it was mentioned "assuming good hearing". I would bet our hearing abilities across the frequency spectrum are all over the place...collectively. "When is the last time YOU had your hearing evaluated?" I agree with asvjerry. Also the set of preferences, qualities or the like ....with what sound should be is also different for everyone. Each of us will place a higher or lower value on such tags as "soundstage, dynamics, bass depth, etc"

Your hearing is only as good as the best HiFi system you ever heard. 

"Stradivarius will sound great in anyone's hands "--this simply is not true.  It takes years to learn to produce a good tone and to play in tune on the violin.  And not everyone who tries achieves that goal even with the years of effort.  So, no, it's just not true.

Right. We live for the chase and thrive on arguments.
Never played Stradivarius but once I did play a very high level custom classical guitar. It sounded spectacular, and my skill as a guitar player is rudimentary. True, violin is a more difficult instrument than guitar or piano, generally speaking, but I am quite certain that this makes no difference. I heard excellent violins played by lousy musicians.

geoffkait, Absolutely.  And then it was subject to the space it was in, how it was set within it, the materials within that space, the equipment combination....were there others in the room (audio show 'extravaganzas'), what was being played, any predispositions you may or not have held at that given time....
inna's 'processing of perceptions' seems rather apt to moi'.  I'm sure we as a group could essentially agree when a 'system' behind a curtain sounds like pounded poop.  It's when we reach the 'extremes' of our selection of equipment and the above variables I've noted that we launch into our perceptions of what we're hearing....this 'n that nuance, shortfalls, strident, 'forward', 'restrained'...we begin to parse ourselves into our subjective perceptions of what and how is happening to our ears, inside our heads.  And 2psyop is right in that respect....we listen with our brains, or what's left of them, given modern uncivilization and the daily dose of it.  We'll agree on some aspects, argue endlessly on others of what we 'hear'.
And then there's our 'listening systems', the ones our DNA has gifted or cursed us with.  I find it fascinating that there are people who apparently relate what they hear as colors....I can't do that.  My spouse says I can't hear her at all, but that may just be 'selective' on my part. *L*
I know my hearing is faulty, due to age and abuse.  I have mild tinnitus, which I only have full awareness of when I go to bed.
As for what's in my skull...having had an MRI recently of it, I can verify that at least there's something in there.  I got a cd of the imagery as proof of some content.  Function?  Well, there's something else we could argue about...;)
My personal 'system' can't be regarded as 'high end'.  I don't have the budget to pursue such, and frankly I'm not interested in the pursuit of it anymore.  I do know what I like to listen to, and have my own thoughts as to how to attain that, given the space I have to work with.  Within that envelope, I listen to what I like to spend the time doing so.
In some respects, IMHO, we're alike in that pursuit. *S*
It should be the music that's important.  The 'how' to do so is up to the individual to decide what limits to set, where one can 'stop' and be satisfied with that....