I use a heater in the fill water and let it sit a bit. Plus, it's a 55gal tank with two Jäger heaters. Whatever temp difference there is when I add is diluted and quickly brought to nominal.
If you have a larger tank or less time, then yes, I can see you needing hot water as well.
Perhaps the additional hot water tank cruft is no issue.
In the same vein, if you go on bypass you'll only be filling 1/3 softened water. Perhaps better than all-softened water?