Breaking a betrothal isn't quite as severe as breaking a treaty, and isn't that big a deal. No one complained when Joffrey broke his betrothal to Sansa, after all.
Those situations are hardly comparable, however, considering Ned Stark had been executed as a traitor. Of course no one would give a damn that Joffrey's betrothal to the daughter of a traitor was broken so that he could instead be betrothed to the daughter of a wealthy and powerful family in the Tyrells.
As for "relative ease" - even you point out that it would likely have taken "a couple months" for a successful siege against the Twins. Walder Frey was in an excellent position with the location of his castles not solely because Robb needed to pass to wage war against the Lannisters, but because the Twins could easily have closed against the northern army as well if it were in retreat. Agreeing to the marriage was the only way in which Robb could ensure that Walder Frey would remain loyal.
Re: the Iron Throne - Robb had no interest in staking a claim to all of Westeros. After all, his bannermen had declared him the King in the North (or King of Winter, if you prefer). Robb's interest, beyond the safety of his family, was the sovereignty of his own realm, not expanding his power to encompass as much of the Seven Kingdoms as possible.
Re: "technically didn't break his word" - Robb agreed to the marriage, having vested in his mother full authority to negotiate in his name. He broke his word, period.