The presence of a keel isn't necessary - just righting moment. If you look at most very large sailing ships, their keel isn't a large protruding fin keel like on racing boats like you're imagining. A cargo ship has enormous righting moment just by means of its ballast - the windage of their hulls alone is enormous.

I still don't think using traditional sails is practical though, and kites are a far more elegant and useful solution. They require far less cost and are easier to retrofit onto existing hulls, can be easily scaled up or down depending on wind conditions, and in the event of even catastrophic failure are pretty safe (i.e. if the kite line were to break). The biggest danger of them is the kite line falling in the water and getting fouled on the propellers, but this is a solvable problem.