It's a question that people used to ask about Black Morass a lot too (indeed, the first boss, Chrono Lord Deja, will ask you that himself), but Black Morass was a little more cut-and-dried. Medivh unquestionably cost many lives in bringing the first Horde through his portal, but if the orcs never set foot in Azeroth, then the world would have fallen to the Legion. The Bronze Dragonflight is unusually blunt about the cause-and-effect; war breaks out among the human kingdoms, the Alliance never occurs, the new Horde is not present at Hyjal to defend against Archimonde's forces -- indeed, the Legion may very well have swept the world without Hyjal ever occurring. So, despite the destruction wrought by the first Horde's entry into Azeroth (and you could argue, because of it), Medivh must succeed in opening the portal.
I'm not sure it's quite that straightforward with "Old Strat" -- and questions about whether it is prompt some thought-provoking questions concerning Azeroth's past, present, and future.
Now, I haven't done Culling of Stratholme yet, so anyone who has, feel free to chime in, but these are the reasons that my guildies and I came up with for why Arthas' descent into troubling moral waters can't be stopped when it starts:
The Bronze Dragonflight just doesn't want to mess with the timestream.
Reason enough, and the reason given to you by Chromie for both quests she'll give you for the dungeon. Bad things happen when you mess around with time, and that's the excuse also given by a member of the Kirin Tor, Archmage Timear, when he sends you to old Strat for the daily dungeon.
Do they? I'd feel a lot more comfortable if the Keepers of Time could come up with a concrete reason for why Arthas can't deviate from his path to Icecrown, or if they had jack to say about what Nozdormu is really up to. More on this in a moment.
If Arthas never travels to Northrend and/or gets Frostmourne, there's no one to: a). provide crucial information for Illidan when he needed it, or b). stop Illidan later.
Illidan destroys Tichondrius, the former leader of the Nathrezim with the Burning Legion, in part because of information Arthas gives him concerning the skull of Gul'dan (which Illidan goes on to consume, thus becoming the demon/elf hybrid you see in the Burning Crusade cinematic). If Illidan hadn't run into Arthas at that point, Tichondrius would almost certainly have killed off the Night Elves and then wiped out everything else he could find.
But Illidan and Arthas don't actually like each other, and they like each other even less after the Legion realizes that Nerz'hul (the actual Lich King) has gone rogue and that the Scourge are no longer under their control. If Illidan had succeeded in destroying the Frozen Throne during the events of Warcraft III, the Scourge would have ceased to exist as a counterweight to the Legion's power (bad) and Illidan, still smarting over his long imprisonment and in command of Kael's elves and Vashj's naga, would not have had an effective foil (also bad).
You can see a late example of this in the demons battling the undead around the Shattered Sun Offensive's staging area at Sunwell Plateau; it was a lot better for these two powers to be occupied with each other than it was for them to be occupied with us.
People tend to refer to Arthas as the Lich King without acknowledging that he's (at best) half of what occupies that suit of armor. Ner'zhul, the onetime elder shaman of the Orc clans on Draenor, is the real brains of the outfit, and nobody knows his real agenda. He's accomplished great evil over the course of his existence -- but not all of it was intentional, and he tried to stop the rise of the first Horde after he realized he'd been duped by Kil'jaeden. His actions as the Lich King may well conceal a higher purpose -- though, given the destruction he's wrought, that's a pretty hard sell -- but there's no denying that the entity once known as Ner'zhul the kindly shaman has been entirely devoid of compassion or pity over the span of his existence.
Some greater threat yet faces the world that requires the Alliance and the Horde to remain united.
Somewhat doubtful in light of the events concerning Angrathar but still a possibility.
Nozdormu -- if he is in fact the leader of the Infinite Dragonflight as is hinted ingame -- is trying to alter the past because Arthas plays a role in his (Nozdormu's) death.
I actually find this to be the most interesting possibility by far. If Nozdormu is responsible for the Infinite Dragonflight, he's playing pretty fast and loose with a number of important events in Azerothian history, somewhat akin to the fashion in which Malygos has gone nuts on the use of magic.
Nozdormu knows the time and place of his own death and may be using the Infinite Dragonflight to disrupt the events that lead to it. There are four events that players are currently able to affect in order to restore the timeways: Thrall's escape from Durnholde, the opening of the portal that first brought the orcs to Azeroth, the events of Mount Hyjal and the end of Archimonde, and now Arthas' descent into evil. I don't know whether there's a common thread linking all four events beyond the obvious need for the existence of the modern Horde, the existence of the modern Alliance, and some sort of vague note on Arthas' rise as the Lich King. Beware, Nozdormu; you too could become a raid boss.