Nonsense. Now you are talking like Eddard. Tywin was either in open rebellion against the Crown, or The Mountain acted on his own and was a bandit. There was no "making matters worse". By definition, it couldn't GET worse. What it could get, was BETTER. Better was allowing Loras Tyrell to go off and either kill the Mountain or be killed. Either way, the Throne would win.
It's that simple. Sending Loras was a win-win scenario. Eddard was a fool who thought preventing further open hostitilites was a thing to be avoided, rather than embraced.
Ok, I'll give you that. But I don't get how that has to do with honor. Mayhaps I am sounding like Ned, but I don't see how a desire to prevent further open hostiles is a bad thing.
Also, it is entirely possibly that the Loras thing would not be win-win. Mace is apparently easily manipulated, and the Lannisters are better at that than Ned. Consider this - Tywin figures, ok, I'm screwed otherwise. Cut Gregor loose, and send envoys to both Martell and Tyrells. To the Tyrells - hey, Ned Stark send your son to get his head smashed in to slow your rise to power/revenge for siding against Robert back in the rebellion. To the Martells - by the way, I think we found who raped and murdered Elia and her children; you can have him if we can take him from Ned Stark. Now Ned, by following your advice, has potentially three of the most powerful Great Houses lined up against him.
Now, I can see the possible benefit of sending Loras, but it's not as clear-cut win-win as you make out. The safer option was send a Lord who was loyal to Robert first - Lord Beric. Hindsight being what it is, it turned out to be a poor option, but I don't think you can dismiss it out of hand as a problem with Ned's honor.
Eddard was the Lawful Regent of the Realm and the Lord Protector of the Seven Kingdoms. He didn't have to justify his actions to anybody. As long as he held the "Baratheon children" as his wards and Cersei as his "Honoured guest", Tywin was screwed. If Tywin moved openly against the Crown, he could threaten to put Cersei on trial for incest (and do it if Tywin didn't actually back down).
Legally, perhaps he didn't require justification. But to quell the rumors? To prevent further uprisings? To anyone not intimately familiar with the situation, this is a guy who rebelled against the last King, left King's Landing as soon as Robert took the city (rumormill: was their a falling out?), kicked Mace Tyrell from around Storm's End, retreated back to the North, only to come out to put Balon Greyjoy back in his place, and then returned back North, and then after the last Hand died of mysterious/sudden circumstances, came to King's Landing, and just a short while later, the current King dies leaving the man who would otherwise have no claim to the throne in power. You don't think more than a handful of people might find that suspicious?
Most lords aren't as honorable as Ned. Most lords seem to want to accumulate power. Most would also suspect other lords of wanting the same. In Ned's case, they'd be wrong, but there are likely several who would think wrongly. Maybe here I can see his honor being the problem - Ned wanted everyone to know he had legitimate and just reasons for doing what he was doing so they wouldn't question him (and maybe even support him), rather than let these sorts of rumors fester and potentially undermine the kindgom. But I'm not convinced that his honor was his sole problem in this regard - honor didn't keep him from noticing all the players around him, that's purely a result of him being a completely neophyte at King's Landing politics.
What seizing the Baratheons as Regent provided to Eddard was TIME.
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That Ned did not stop to consider these things, let alone evaluate and then discount them as options, was pretty much just his honour getting in the way of Peace, Order and Good Government.
That is quite the pretty picture you lay out, and although I could quibble with parts of it, I don't think any of it would be outside the realm of possibility with the knowledge the players of the game had at the time.
I still, however, can't say that his missing of this possibility is due to his honor; at least not solely. Ned thought he had other options; he thought the Renly option was too risky compared to those. Yes, his honor led him to give Cersei a chance to do the right thing, but he didn't offer it blindly - he thought he had back-up. That key thought there is why I can't say it was his honor that led to his downfall. Not entirely. It was the fact the Ned completely misread every other player in King's Landing, and that was due to him being politically stupid, not his honor.