It wasn't the ship that was too advanced, it was the writing, which was a) still in the TNG era mindset, and b) as stated hamstrung by studio dictates that the show be recognisably Star Trek.
I would have gone a lot more primitive with the ships, modular with a warp drive section, a central spinning habitation and arboretum module (not enough energy for artificial gravity across the whole ship while in warp), also producing the ship's oxygen and food, and a forward impulse powered contact/combat section, which would detach and explore systems while the main ship waited outside the Oort cloud. Weapons would be railguns and missiles, and transporter tech would be limited to cargo transporters only. For shielding the only option would be to increase power to the deflector dish, so the energy field meant to divert interstellar particles away from the ship, could also handle more energetic material like enemy railgun shells, and maybe lasers (the ship could also have a mirror finish).
And Brexit would mean Brexit. I mean Warp 4 would mean Warp 4, the 9 hours to Neptune and back would play into the 'real world' so weeks and months voyaging between systems not hours and days. The show would by necessity be an anthology show, covering a fleet of exploration contact ships, so while one ship might be in transit, you'll catch up with another ship as it makes system fall around another star, or an interstellar contact. 20 light years around Earth would be known space, Earth colonies and other powers, 40 light years would be the Final Frontier of the mid 22nd Century. Vulcans would be our friends, enemy powers would be the Andorians and the Tellarites, and the Centaurians would be neutral. I dunno if the Centaurians would be native to Alpha Centauri, or whether there would be a mass exodus from Earth following Cochrane's discovery and the post atomic horror, and the millions who emigrate to Centaurus over the first hundred years, find remnants of an alien civilisation there and find some tech advancements, dilithium, real shielding, better computers, maybe even some salvagable ships, enough for them to declare independence from Earth within 50 years of colonisation. Vulcans have faster ships and better sensor technology, Andorians have better weapons technology and better artificial gravity control, Tellarites are better ship builders and have a bigger trading fleet, and transporters rated for lifeforms. Humans are more adaptable and advance quicker than everyone else. Of course the show's about the creation of the Federation. How these races can be stronger together, despite and because of their differences.
No Borg, No Klingons, No Ferengi, and definitely no time travel.