It is during the engagement period that man's fidelity to his spouse is least in danger. The longings and expectations of closeness create a feeling of attraction and loyalty, so we do not have to be as stringent with such a man. The Torah is not worried he will look at another woman, but rather that he may die in combat, and another man would end up marrying his fiance. It is as if Hashem is bonded to Israel with the love and loyalty of the engagement period. The connection of Israel and the Torah is a bind made by choice and love, much like the binds of engagement.
Marriage is a whole different story.
After the couple is married, there is the constant fear of a loss of loyalty, and that is why the Torah commands us to leave the bridegroom at home for a full year after he gets married, so that the couple can build bonds of trust out of their constantly being with each other. This is why he is free for the whole year, and does not even participate in the war effort, not even helping to repair the roads. It is a similar reason for a man who has just built his house. The Bnei Yissachar writes that the mezuzah is the symbol of loyalty between the members of the house, and this is alluded to in the word mezuzah itself. The word mezuzah contains both phrases within it.