I actually really like that the "to bodly go" monologue is an in-universe quote attributed to the man who invented the warp drive. Connections like that between shows can sometimes feel a bit to fan-service-esque but I think its a logical idea.
I was one of those that watched TOS long after I watched all its successor shows and First Contact movie, so I was unaware and surprised when I saw the episode Metamorphosis, discovering that Zefram originated from TOS all this time. Same would apply to the likes of Surak, Kahless and Col Green for the TOS episode The Savage Curtain.
Cochrane was from Alpha Centauri, a descendent of Preserver-transplanted humans. The retconned lore that made him an Earth-born human turned me against Trek entirely. It made no sense that when every other facet of ST:TOS was carried over to TNG that they changed this for no legitimate reason. The Vulcans gave humanity warp drive - period. No human could have possibly developed it at that time, and certainly not in a post-apocalyptic barn in Montana.
Zefram Cochrane can't hold a candle to the greatest Carogan of all time; Bird O. Prey V; who crashed more vessels than the entire Alpha Quadrant put together.