After vacuuming and wiping down with a disposable dusting cloth, I mist Bono Floor Cleaner and follow with a steam cleaner (towel wrapped around a floor vacuum-type tool, frequently turned as the towel picks up dirt). When done, the stack of towels goes straight in the wash with a touch of bleach. I'm not sure if those steam mops would be sufficient...I used a Shark steam mop once and it was worthless. A real steam cleaner is somewhat expensive, but has many uses around the house and in the cars.
Here's the thing with a real steam cleaner...it will generate >60 psi and >250F steam at the tip of the nozzle. But when cleaning hardwood floors you don't need the quantity or the high temp, and frankly, when you connect the 4 ft of extensions, the floor tool with the requisite air pocket under the towel, your pressure and temp drops significantly. So it's very well possible that some steam mops would do an equally good job as a good steam cleaner. Can't say which though. Obviously, the steam mop would only have one purpose though.
As to the Bona, I'm not convinced it does much more than water, so I'm burning through what I have left and not inclined to buy more. In the future, I'll probably mix household vinegar and water in a 1:10 ratio and spray that in place of a floor cleaner, then follow with the steam cleaner. The vinegar/water mix is an all purpose cleaner around the house.