Actually, I vacuum hard floors with a mini cannister vac instead of sweeping before mopping and find it easier, just a YMMV thing. But it doesn't push hair and dust particles up into the air like a broom does, and it doesn't leave little escapee dust balls and dusty streaks in corners and against walls and furniture. It seems that the house is less dusty after switching from sweeping to vacuumming, but again, it might be just my perception. I only use dustmop and swiffer at home for quick sweeps down the middle in the track areas.
Again, my main focus for mopping is to get the floor C-L-E-A-N. If you spill a little water on a freshly mopped floor and wipe it up with a white cloth, that cloth should still be white afterward, or the floor isn't clean. Rinse water should come out clean. I used to write articles for an internet newsletter with 5,000 subscribers. When questions about streaking floors came up, I'd advise them to focus the weekly mopping routine on getting the floor a) cleaned of all dirt and b) rinsed of any detergent residue. Everyone that ever reported back later told me this resolved the problem. This level of clean mostly counts in homes where there are small children on the floor or if the family has allergies to dirt and dander. It's the difference between "looking" clean and actually "being" clean.
The bottom line is that if swipes and spritzes yield satsifactory results for your family, then that is really all that counts.
