But Ned had other choices.
Loras asked Ned in front of hundreds of witnesses to lead the expedition to capture or kill Gregor Clegane. Ned refuses because as Loras is only a little older than Robb, Ned has trouble seeing Loras as a grown man. Loras lacks experience. Ned correctly perceives that Loras is motivated more by personal glory and revenge against Gregor Clegane than by honest outrage over lawbreaking and atrocity. Ned thinks that Loras would simply get himself killed. Instead Ned orders off most of his household guard and you know the rest. Ned just didn't think this through. Ned has already been attacked in public by the Lannisters and received no help from the City Guard. That's a pretty strong indication that neither Ned's status as Hand (although technically he wasn't Hand when he was attacked) nor the fact that he's Robert's best friend and Warden of the North deter the Lannisters. So Ned's first move should be to keep his remaining retainers very close as they are the ONLY people he can trust in King's Landing. Ned has no other allies at this time.
Ned may or may not know about the sexual relationship between Renly and Loras (I can't recall myself) but he must know that they are good friends. Ned also must know that Loras is Mace Tyrell's favorite son, albeit not the heir (in the book). Ned didn't know the depth of Stannis' and Renly's dislike for one another. Ned didn't know yet about the Lannister incest. Ned would have been much wiser politically to send Loras. If Loras is able to capture or kill the Mountain, then Ned gets credit for giving Loras the chance to shine. A happy Loras means a happy Renly and Mace. If events still occur later as they originally did then Renly might even help Sansa and Arya get out of King's Landing rather than only looking to save himself.
If, as is much more likely, The Mountain makes Loras his hand puppet and kills him in a particularly gruesome and painful way both the Tyrells and the Renly faction of the Baratheons are out for blood. Renly is thinking less about crowning himself King and more about revenge against the Lannisters. If he still leaves King's Landing he doesn't waste time dillydallying with tourneys and games but immediately starts war. Even if Renly still decides to crown himself and is still murdered by Stannis, the Tyrells simply wouldn't join with the Lannisters afterwards. Even if it makes political sense it's almost impossible to do. The Tyrells probably just go home or (less likely) swallow hard and reluctantly support Stannis. So at the Battle of The Blackwater there is no Tyrell-Lannister joint attack. This means Stannis takes King's Landing. Heck without Loras to whisper sweet nothings into his ear (mostly an invention of the show) there's an outside chance that Renly doesn't declare himself king. Stannis and Renly remain unified. If Stannis declares himself earlier then Robb Stark never accepts the King in the North title. Because he's aligned with two of the most powerful Southern families and isn't seeking to secede, Robb doesn't need Greyjoy allies. He never sends Theon home which means Winterfell isn't burned nor are his younger brothers believed dead. Bolton and Frey don't have the guts or the inclination to start acting up because the Lannister position is MUCH weaker. Heck, Lysa might decide (or have it decided for her) to join the likely winning side and commit the Arryn legions to the Stark-Baratheon-Tully-Tyrell group. Even Tywin would have had to sue for peace.
If Ned still has his houseguard (assuming he still foolishly warns Cersei of his intentions and he probably would) there's a slight chance that Sansa and Arya get out of KL and a better chance that Ned WINS the showdown in the throne room. If that happens and Ned has Cersei and her children at his mercy Tywin would have to proceed much more carefully. Full war might never have broken out. It would still be tense though as Ned would not want the Lannister kids killed no matter what while Renly and especially Stannis would be very much in favor of that. Maybe Joffrey is sent to the Wall while Myrcella and Tommen are fostered in the North somewhere? Of course although Littlefinger wanted war and got it, Varys didn't want it yet. So who knows what moves they would have made to counter this. So small decisions like who to place in charge of a military expedition have huge consequences. Obviously no human can see how all the dominoes will fall, not even Littlefinger. You can't blame Ned for not foreseeing all that would happen. But even if Ned didn't appreciate the political wisdom of cynically binding the largest House to his cause, he should have understood the personal benefit of keeping his guardsmen close. So it goes.