Washing a stained and sealed concrete floor is a lot like washing a vehicle. If you tried to just wash your car with a mop without drying it, it wouldn’t work very well. Your floor is no different.
For routine cleaning, you can mop it, then shuffle around with an old towel (taking up the dirty water) and get it clean fairly quickly. If you are cleaning a commercial floor and towels seem unprofessional, microfiber mops that start dry and get wet on the heals of your wet mopping work great.
If your floor is outside, think drive-through car wash. That is get the dirt into solution, rinse it, then break out your leaf-blower to blow-dry the dirty water off.
If the floor is really dirty, think gas-station-window washing. You need to get the dirt into solution and then squeegee the water to a wet-vac and just use the mop or towels like you would use the paper towels at a gas station. Remember the windshield analogy - it's all about the squeegee. If you scrubbed your window, and used a shop vac to pull the water off, it would require a lot of paper towel action. If you are a pro with the squeegee, you can get it fully clean in the time it takes your road-tripping companions to buy chips and drinks.
Soap is a great invention, and the best soap for your finished concrete floor is surprisingly cheap. The goal is generally to clean the floor without leaving a film or removing the finish, so mild or highly diluted detergents are best. I recommend anything that starts with “Neutral” or “Neutra-” from a janitorial supply store - NeutraClean, Neutral Quat, etc. If the smell of Thyme is more appealing the 3M smell, try Seventh Generation,. Here is a link that I'm not set up to get paid on: