No Warp Zone
The No Warp Zone (commonly abbreviated as NWZ), is a 50gms area surrounding Starbase One in which it is forbidden for ships to engage their warp drives. While it is commonly observed by both incoming and outgoing ships, many Starfleet Captains choose to ignore it on outbound departures from the Starbase, to the chagrin of Starfleet Command
The NWZ is not a uniquely Federation concept, as the Romulan Star Empire has a magnificent No Warp Zone of a whopping ten GMs. However, in practice, the Rihannsu ships are fond of coming into dock as quickly as possible, at warp 1 or greater.
The NWZ was the brainchild of Clayton Stabu, and was established in 1996 when he was Rear Admiral and head of StarFleet Base Command. While a common belief holds that the NWZ was established as the result of one or more accidents that took place near Sol, in reality it was established in anticipation of any accidents and was meant as a traffic control device. The original NWZ was 6 times larger than the current version, but was reduced after loud complaints by StarFleet Captains.
Basically, here's the reason the NWZ exists. Way back in 1996, space was offline while the latest version (TOS Space 3.0) was being readied. This would be the first version of space in which collisions were a possibility (previously it was not unusual to deliberately fly through a planet to reach the other side...if a ship found itself with Earth between it and a safe docking berth on Starbase One, they'd just fly directly through Earth to get there.)
There was concern about collisions, since no one knew how hard or easy it would be to avoid them. (As it turns out, it's pretty easy, but they happen a lot anyway. See this Note on Collisions.) Back then, no one had imagined that the big problem would be crashing into stars or the random planet here and there. Stars and planets are pretty big, and it was hard to imagine hitting one by accident (ah, the innocence of those days...) Anyway... so in trying to come up with a way to anticipate and avoid collisions when the new version of space came online, the consensus in StarFleet was that the biggest danger would be two ships approaching the base to dock at the same time, or (perhaps even worse) one ship undocking at the same moment that another was just about to dock. See, there was so much excitement over the creation of the new space system, that we were sort of expecting TOS's membership to expand dramatically after it came up, and there were visions of LOTS of ships, both civilian and military, zooming around the vicinity of Sol system and Starbase One.
So Clayton Stabu, who was commander of the base at the time, came up with the idea of the No Warp Zone, and pitched it to Fleet Admiral Robert Morse, who approved it. The actual NWZ regulations were rather complicated and reflected the concern of traffic jams around the base and multiple ships attempting to dock or undock at the same time (which later never proved to be a significant problem). There was all this stuff about approaching ships halting at the outermost boundary of the zone, and orbiting the base in a counterclockwise direction until given clearance to approach, and right-of-way belonging to departing ships, etc etc. All that survives to the present is the fact that you can't go to warp within 50 GMS of the base.
Why has it been retained? Well, this author, for one, honestly never thought seriously about abolishing it, mainly because it was one of those things that was just always sort of there, even though it was pretty damn annoying when you were a starship captain. Probably if anyone really stopped to think about the fact that there's no useful purpose served by it, it might get abolished, but then, it IS a sort of long-running relic from the past (it's existed for 9 years, after all.) And so nostalgia alone might be enough reason to keep it. Or, it may give the people unfortunate enough to be assigned as full-time crew to Starbase One (a job only slightly better than working at StarFleet Academy, for the most part) something to do, as they can yell at captains who flagrantly violate the NWZ.
It IS true that a strict adherence to the NWZ might have saved USS Republic, but her problem was really that she was using autopilot to approach to docking range, and even at impulse might still have exploded. But her crew might have had more time to notice they were going to crash. Or not.
Anyway, there's no really good reason for it, it wasn't created because of any of the many crashes that have occurred over the years (although this may have been a convenient explanation for its existence), and it could probably be done without. But it's there. So there.