It's not throwing out anything. It's a BIG Galaxy (even "local" space) and a huge Starfleet with hundreds of ships and crews. Why must every one of them have ties and references to prior series characters? You can have a series that is obviously in the same fictional universe without once referring to Janeway, Riker, being related to Spock or meeting a younger version of the lead of the original series. As long as the writing and actors are strong, as long as it adheres to the Spirit of Star Trek, it will get an audience. I don't mind occasional callbacks or reminders that it's all one continuity, but the Nostalgia Button is worn down to a nub.
But, again, this is just me. Lots of fans love it. I envy them, I wish I did
There's not ever going to be a Star Trek series that exists in a vacuum.
TNG - "An all-new Enterprise with an all-new crew!" Still the Enterprise. They tried having Ferengi as the main villains and that bombed spectacularly, so they went back to the Romulans. Q is Trelane by another name, but done better. Riker and Troi are Decker and Ilia with different names. Data is a cross between Xon from
Phase II and Questor from
The Questor Tapes.
DS9 - The Cardassians were created for TNG, the Bajorans were created for TNG, then they used those aliens as the basis to build the framework for DS9. When TNG ended, all the Galactic Alpha Quadrant Politics with the Federation, Klingons, and Romulans shifted right over to DS9. Two of the main characters, Worf and O'Brien, came from TNG.
VOY - The Maquis were created for VOY, but their storyline was introduced in episodes of TNG and DS9. The Doctor was based off of Moriarty. Q, Barclay, and Troi all eventually became recurring characters. VOY's biggest enemy was TNG's biggest enemy: The Borg.
The TNG Movies, DS9, and VOY are all extensions of TNG; and split everything three ways. Each one got a different piece.
ENT - This series shows the aftermath of what happened 90 years after Vulcans made
First Contact with Humans. So, in a way, ENT is a follow-up to FC. The ship they're on is the Enterprise, NX-01, leading to a string of Stupid Prequel Arguments. They run into the Klingons and the Ferengi, leading to even more Stupid Prequel Arguments. (Can you tell I'm not usually a fan of prequels?) The entire fourth season was devoted to showing how things will eventually lead into TOS and TNG. And you guessed it, more Stupid Prequel Arguments. "In the Mirror, Darkly" was equal amounts Mirror Universe and Big TOS Parade. Framing "These Are the Voyages" are Riker and Troi on the Enterprise-D as if it's still TNG Season 7, which
actually is what some people like to pretend
Picard Season 3 is.
The point is: None of these series existed in a total and complete vacuum, even during the Berman Era.
To your credit, though, at least you're being fair in your critique. SNW and PIC Season 3 are two sides of the same coin. One with TOS, the other with TNG. A lot of people have blinders on and will attack PIC S3 for "Nostalgia! Nostalgia! Nostalgia!" while giving SNW a free pass, even though it has a ton of TOS characters, TOS enemies, and will most likely ultimately end up showing how things got to TOS.
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But if people want next-to-no callbacks and minimal fan service:
Discovery Season 4. You get exactly what you want and a Roddenberrian Plot where communication saves the day, while trying to stop an all-powerful Species 10-C, which is from another galaxy and doesn't recognize humanoid life.
The hugest complaints about
that season were that it was "too slow" and everyone was "talking about their feelings". Not exactly the Non-Stop Action Jackie Chan Movie that certain people want to make New Trek sound like it always is.