There should be no harm to fish if adding water straight to the tank is done properly.
I have been doing this for many years and have never lost a fish to a water change nor has my parameters been any different.
I firstly turn off all filtration ensuring that the new water does run through the majority of the bio systems
I then ensure that I match the tap water temperature as close to the tank water as I can - just judging by hand under the water.
I then add the total tank volume worth of Prime as I commence the refill and add another cap at the end for safe measure. There is always a powerhead going to circulate the water mixture with the Prime. I let the water to mature for about 10mins as another safety measure
After the 10mins I turn on all filtration
I have tested parameters right after and an hour later when I first began doing this and was happy with the results. This made me confident in this method.
If anything - the fish love the new water from their reactions
