Torah Scholars and Peace

The final passage in Berakhos (64a) is famous, largely because it is recited towards the end of Shabbos morning prayers:

אמר רבי אלעזר אמר רבי חנינא תלמידי חכמים מרבים שלום בעולם שנאמר וכל בניך למודי ה' ורב שלום בניך אל תקרי בניך אלא בוניך

R. Elazar said in the name of R. Chanina: Torah scholars increase peace in the world, as it says, "And all your children will be taught of the Lord, and great shall be the peace of your children." Read not banayikh (your children) but bonayikh (your builders).

I never understood why the last part of the passage is necessary. The verse states that all of the children will be scholars (children=scholars) and that the children will have great peace. If when the children become scholars is when there will be peace, then the more children are taught then the closer we come to that time. Therefore, those who teach Torah are bringing peace. (Or, perhaps more understandably, are bringing us closer to the time when there will be peace.)

What does the final line about builders add? And which banayikh (children) is supposed to mean builders, the first or the second? If it were up to me, that last line would be erased. Actually, if you look at the other four times in the Talmud where this passage appears (Yevamos 122b, Nazir 66b, Kerisos 28b, Tamid 32b), they do not have that last line.