Star Trek and Stargate both go by the premise that “anything that can happen does happen in alternate quantum realities.” It’s just that the characters from those realities assert that their version of reality is the only one that matters (which is an actual quote from Teal’c.)
The Prime Universe does still exist. As does the universe in Yesterday’s Enterprise and the Mirror Universe. To say that Prime does not exist is to say Mirror does not exist; and the Mirror Universe’s timeline, which is wholly separate from Prime, was accessed repeatedly by Prime characters (and vice versa) during the events of Deep Space Nine, not to mention TOS and Enterprise.
Star Trek 2009 nine makes it clear that the Narada when back in time, altered history and thereby turned the prime universe into the Kelvin universe. There may be an alternate universe that is exactly the same at the prime universe, but it would only be a duplicate universe and not the prime universe. As far as I know, Discovery does not take place in an alternate universe that is a duplicate of the prime universe, it takes place in the prime universe itself.
It actually specifically makes the opposite clear. The Narada created a divergent timeline that they call “an alternate reality”. The Prime universe is still there, untouched (just without Romulus). See also: Star Trek Online, which continues in a post-Romulus Prime timeline.
No where in Star Trek 2009 does it say that the Narada went to a different universe, it just went back in time and changed history.
As for Discovery, it takes place in the Prime timeline. Nothing about the content of the plot has contradicted anything in the timeline that I can see. The visual changes should not be explained away in-universe, like Enterprise tried to do with the Augment Virus. This is how it looks in a show made in 2017, just as it should. As fun as the fan films are with their 100% accurate sets and makeup, that isn’t want a modern trek should be. It SHOULD be pushing the envelope for effects and prosthetics and telling stories that are relevant to today, and you know what, Discovery is doing exactly that.
I disagree. If you want it to be “how it looks in a show made in 2017”, then call it a total reboot, totally having nothing to do with the original cannon. But if you are going to put it in the original cannon, it should look like it.