Ph and total dissolved solids (tds) are not necessarily directly linked, and well water with lots of CO2 dissolved has essentially the same tds right out of the tap at 7.0 ph as it does after it reaches equilibrium with the atmosphere and has 7.8 ph. There is only a risk of "ph" tds shock from using your water right out of the tap if the tank water tds has increased sufficiently to be a problem. Again as long as you are doing enough water changes using tap water immediately is not an issue, because the CO2 caused ph shift you are seeing from tap to day old tank water is NOT a change in tds. Osmotic pressure changes due to tds differences is the cause of the "ph" shock people talk about.
Water softeners work by exchanging ions for other ions, but because what they are pulling out has a 2 charge and the exchange salt has a 1 charge the water that comes out is "softer" but has a higher tds by double the component of the minerals responsible for hardness. Generally for fish, what we would call hard water is easier to deal with than the higher tds water that comes out of the softener. And some of the things that make up hardness is needed by the fish, plants, and your beneficial bacteria. So non softened water is healthier for the fish generally.
Water temperature of change water is not as important for river and stream fish because a good thunderstorm can drop the temperature 10-12 degrees F. Assuming you change 50%, your tap water can be as much as 20 degrees F below your tank temperature and that would simply simulate a good thunderstorm because the total drop is half the difference between the tank and tap temperatures at 50% change.
Example: tank temp 78F
tap 58F with 50% change= good thunderstorm
tap 53 with 40% change = good thunderstorm
tap 48 with 1/3 change= good thunderstorm
tap 38 with 25%change = good thunderstorm
Ice water with minimal ice 20% change = good thunderstorm
I'm not recommending doing water changes with ice water, but what I'm getting at is that the net change in tank temperature would not be beyond what a thunderstorm could cause. I've seen that temperature drop act as a spawning trigger. Given that the heater would be running in the above cases, I don't see any issue with piping the change water right in. The refill time period, unless you are refilling with a fire hose, would be enough to take care of water a bit colder than what you might use to simulate a "thunderstorm".
Lake fish do tend to have a more stable environment given a choice of habitat and thus you might limit the temperature variation due to water change, but again I don't know that it is necessary to match the change water temperature with the tank temperature. You can find reasons and fish that need more of a temperature match, but for general community tanks it isn't as much needed.
Water softeners work by exchanging ions for other ions, but because what they are pulling out has a 2 charge and the exchange salt has a 1 charge the water that comes out is "softer" but has a higher tds by double the component of the minerals responsible for hardness. Generally for fish, what we would call hard water is easier to deal with than the higher tds water that comes out of the softener. And some of the things that make up hardness is needed by the fish, plants, and your beneficial bacteria. So non softened water is healthier for the fish generally.
Water temperature of change water is not as important for river and stream fish because a good thunderstorm can drop the temperature 10-12 degrees F. Assuming you change 50%, your tap water can be as much as 20 degrees F below your tank temperature and that would simply simulate a good thunderstorm because the total drop is half the difference between the tank and tap temperatures at 50% change.
Example: tank temp 78F
tap 58F with 50% change= good thunderstorm
tap 53 with 40% change = good thunderstorm
tap 48 with 1/3 change= good thunderstorm
tap 38 with 25%change = good thunderstorm
Ice water with minimal ice 20% change = good thunderstorm
I'm not recommending doing water changes with ice water, but what I'm getting at is that the net change in tank temperature would not be beyond what a thunderstorm could cause. I've seen that temperature drop act as a spawning trigger. Given that the heater would be running in the above cases, I don't see any issue with piping the change water right in. The refill time period, unless you are refilling with a fire hose, would be enough to take care of water a bit colder than what you might use to simulate a "thunderstorm".
Lake fish do tend to have a more stable environment given a choice of habitat and thus you might limit the temperature variation due to water change, but again I don't know that it is necessary to match the change water temperature with the tank temperature. You can find reasons and fish that need more of a temperature match, but for general community tanks it isn't as much needed.