Must speakers have certain volume to sound convincing ?

In my opinion, "yes". If a speaker isn't adequately "pressurizing"  the listening environment it doesn't sound "convincing". In my experience I've found that there typically is a "sweet spot" volume - much like a sweet spot listening position. To low a volume or too high a volume simply does not strike the same "chord" in me as the "right" volume. And the "right" setting is also a variable depending on many things such as the type of music, particular song, and even the time-of-day/night.

My EgglestonWorks Fontaines do need a kick in the pants to sound good. For me, not that the room is inadequately pressurized but seems more like the drivers, which are quite robustly built, need some power to move optimally. Not so with my desktop Adam F7 Active monitors - they sound exquisite even at low volume.

I think this very much involves the psychology of each person and thier listening habits and enjoyment. I like low listening very much. I also think planars give enough info at low volume for enjoyable sound. Just my opinion...
BTW even my neighbors Sonos speakers sound clear and fantastic at low levels. Not as much bass as my Monitor Audio Bronze but just as clear and articulate.

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.

I agree with gdhal. The system needs to pressurize the room. For the mood, the song, day or night. Even low volumes interact with the ROOM. My small system needs a small room, Main system needs its own room. But my body wants a remote volume control for those needed/ wanted tweeks!! Plan to add one to my Steelhead shortly!