Broadening at the hit is actually standard for most heavy swords used in slashing attacks. If not then the likely hood of the sword breaking when you make contact with an object is increased. Say a person blocks your swing with a shield the recoil could cause the blade to snap clean off due to the weakness created by not being broadened at the hilt.
Nah, what stops a blade from breaking on impact is the fact swords (well, just about every non-katana blade anyway) are surprisingly flexible.
Also, if you really wanted something for chopping/slashing you're going to want the cutting part of the blade to have the most mass. As beautifully demonstrated by the beastly Ghurka Kukri.
Heavier cutting edges bite deeper. Curved edges do as well, more blade per unit of measure.