Must speakers have certain volume to sound convincing ?

I’m assuming by volume you mean volume of dynamic peaks.

Bottom line is some live music is loud and clear so for me speakers should be able to do the same. Otherwise I would feel I was missing an important aspect of being able to enjoy music fully. That’s just me though.

Music in real life occurs at certain volumes. Many factors affect that volume heard in real life such as distance to source.

Some do not like music loud or with loud dynamic peaks like can occur in real life. They are more easily "convinced" I would say.

Myself, I know what live music can sound like and I want it to be able to sound that way at home at least sometimes if not always (prolonged exposure to loud music at higher levels that might be heard is bad for the ears). It may sound lovely at lower volumes in some cases, but in many cases it will only always sound convincing to me at higher levels.

That’s because I enjoy and listen to all kinds of music, from soft and relaxing to loud and in your face. Variety is a big part of what appeals to me about listening to music. I don’t expect or want everything to always sound the same. Good dynamics is key for that.

So like most things it depends mostly because people’s expectations vary. That’s what makes the world go round.

All else held constant, in order to be able to produce flat response down to lower frequencies, you need larger drivers in larger rooms. In the case of "box" speakers you also need larger boxes ie more internal volume. I think its that simple.