It's almost a philosophical question. You must have the proper chemistry in your strike liquor to insure proper mash pH but you do not need that same chemistry in your sparge, makeup or dilution water. You can make additions (or not) to the sparge makeup and dilution water stylistic ions but it must not contain ions that will upset kettle and fermenter pH. There is little doubt in my mind (though there are those who disagree) that the easiest thing to do is collect the volume of water you need for a brew day, treat it all the same way and brew with it by which I mean use it to mash, to sparge and for makeup/dilution if you need liquor for those purposes. To do this you must have figured out how much calcium, for example, you will allow based mostly on how much chloride and sulfate you want to reach the kettle and fermenter but also taking into consideration calciums effects in lowering mash and kettle pH. If you do this the tendency is for pH to fall into line throughout the brewing process: mash pH, kettle pH and wort pH will all be about where you want them. If you take the alternative approach of mashing with one water and sparging with another you must still take these ions' effects into account but now you have two water treatments to contend with. If, for example, you sparge with RO water (as many do) you cannot count on its calcium to lower kettle pH. You must either forgo that benefit or add additional salts or acids to the kettle or sparge water.
The usual objection to doing things with one uniform volume of water is that you will be sparging with alkaline water. You do have to be attentive to this possibility but it will be rare that you prepare brewing water by adding alkalinity to it. There are some exceptions though and in those cases you either withhold the alkali from the sparge water or check to be sure that runoff pH remains low enough up to the point where minimum runoff extract is reached. It often turns out that this happens even with fairly high alkalinity levels in the sparge water.