Dull knives make you use force to cut things. If you're using force, you can lose control. If the knife or the thing you're cutting slips, the knife will suddenly be moving fast. Maybe toward your other hand. When you see huge gashes on people's hands in the kitchen, it's almost always a dull knife that did it.
If you have a truly sharp knife (very few people do ... even most pros get by with blades that are just serviceably sharp) it will cut with little more than the weight of the blade. The only way you'll ever lose control of a knife like this is if you drop it (please don't). Or if you're trying to cut something you shouldn't. When I cut myself on a sharp knife, it's almost always because it was sitting on the cutting board and I reached past it without paying attention. This is annoying and embarrassing, but has never been serious. I also sometimes shave some skin off my knuckles, or shave off a thin slice of fingernail. This is scary but rarely even merits a baindaid.
If you want a very sharp knife—the kind that requires no force—you either have to learn to use water stones or an edge pro. The former is quicker, the latter has less of a learning curve. But they both do the same thing as far as the knife is concerned.
I only keep 3 of my knives this sharp. I appreciate the low-maintenance versatility of a traditional European blade that you sharpen once in a blue moon and just keep banged into shape on a butcher's steel. I have a burly German chef's knife that I maintain like this (for rough stuff), and also a cheap Forschner utility knife. These guys see a lot of action. I can understand why some people would be uninterested in anything more high-maintenance than this.
Very sharp knives can be a bit of an addiction, even if they're not necessary. They do allow some things that regular knives don't. For example, you can do your most delicate cutting (herbs) before you cut anything else. They won't go brown or lose freshness, even if service is 6 hours away. No one believes this, but it's true. Traditionally, cooks have to add herb prep to the dozens of other last minute tasks before service. You can also very easily slice things so thinly that people will assume you used a mandoline. But you probably finished the task in the time it takes to pull a mondoline out of the cabinet and set it up. Fruit won't brown. Onions won't make you cry (at least not as much).
Those Chef's choice machines aren't terrible. The important thing is to only use the coarsest slot when absolutely necessary, like when repairing edge damage. It removes a lot of metal and will greatly shorten the lives of your knives. The machine sets bevels at a pretty stout angle compared to what a Japanese cook would choose. Which is to say, it's about durability, not sharpness. It will do pretty sharp but not very sharp—probably a little better than the factory edge on German knives.
