As for where colonies should be, it somewhat depends on emerging science. Extrasolar Planet finding capability has developed since Trek came out. Hard to integrate it just yet, as many, many local extrasolar planets have yet to be found, especially the ones of greatest interest to Sci fi, which is rocky planets in the habitable zone.
If it turns out that the Alpha/Proxima system has no small rocky planets in a habitable zone, than it won't matter how close it is. There just wouldn't be a candidate planet suitable for colonization.
Except that it's been established since TOS: "Metamorphosis" that there is a human colonial presence at Alpha Centauri. TNG established a University of Alpha Centauri. DS9 referenced Alpha Centauri as an inhabited system more than once, and so did later seasons of Enterprise itself. So it's not a question of consistency with real science, but of consistency with previously established Trek canon. The writers of "Terra Nova" either forgot that the previous series had established Alpha Centauri as inhabited, or didn't know enough about astronomy to be aware that it was much closer than 20 light years away. Given that they didn't even know Rigel was a real star name, I lean toward the latter.
It's clear that, for all the cast and crew, the writing was on the wall for the fourth season, despite Enterprise being UPN's highest rated show. The that that it was banished to Friday nights for its final season and cancelled just before a new standard of ratings would be introduced seems like a strange case of history repeating itself.
Except that "UPN's highest-rated show" is a pretty low bar. Note that UPN itself did not survive long after Enterprise was cancelled. The network was founded with Voyager as its flagship series, and it pretty much depended on Star Trek as its anchor, never really having much else that had the same level of popularity (except maybe the last two seasons of Buffy, but that show's popularity was probably in decline by then, or The WB wouldn't have cancelled it). Once ST was gone, UPN fell soon after. So it's not comparable to NBC at all. ST was just one of many shows in NBC's lineup, and never one of its top performers. But UPN was built around ST to begin with, and ultimately couldn't survive without it.