Three dots is formally correct to skip parts of a sentence or paragraph when quoting another party for an essay e.g.,
The mountain had crystals in it... above the clouds was a rainbow.
Because you don't need to write the whole paragraph you're trying to give evidence.
Two dots is an informal and cute way of implying there is something else to say, except philosophically you don't need to say it at that moment, so it's more of a short-cut, and yes two dots is quicker that three since the latter means something else, formally any-way.
The two dot version is developing its own meaning. Graphically, it's different and reflects how the person is writing. Definitely, our writing, the way we communicate in our lives, and the way we transmit this communication is changing.
So I agree with how two dots is a quick shortening mid-sentence, to cut it all short when you actually don't know what's next or want to keep it open. It's more poetic and a modern thing with social media, iPhones and emails. When you want to be brief and are implying something else. I think it's grammatical implication and meaning is developing.
I use 4 dots for a similar poetic meaning like when you are ending something with an indefinite thought at the end, more of an artistic label.
E.g. “With love....” Sometimes 8 “for lots of love........x”
So the shortened 2 dots is a short pause, when there's no time to get further into it and it's left open-ended. 3 dots is a formal gap with a meaning of omission in formal writing, or meaning you have left out what us to come. 4 dots is an ending, provoking more thought. 3 dots you can also use correctly to change topic...it's the most formally correct if you're writing properly.
From what I've experienced and studied in language, literacy, grammar and literature.
I think there is a new place for two dots and agree some people will misuse it for the formally correct three dots. The shorter, I would use for a thought or informal conversation. When I'm not committing to make a formal '...' statement. Like if texting with a friend while shopping, e.g.
“Do you like the pink dress?” “It's alright.. Maybe lets go to Bondi?”
So this means I'm still deciding, part way through and I'm unsure. I could more formally write
“It's alright...maybe lets go to Bondi?”
To me this is more definitive. It's two different ways of texting/writing/communicating and a different style of writing.
We use two dots knowing three dots is correct so, it does have a meaning and place whether it not it is misused!