A method for acidizing subterranean formations may include providing a treatment fluid comprising an aqueous carrier fluid, an acid, and a chelating agent comprising N-(phosphonomethyl)iminodiacetic acid, the treatment fluid having a pH at or below that at which carboxylic or phosphonic acid groups of the N-(phosphonomethyl)iminodiacetic acid are protonated and the chelating agent is ineffective for complexing a metal ion; introducing the treatment fluid into a wellbore penetrating a subterranean formation comprising a carbonate mineral; reacting the acid with the carbonate mineral in the presence of the chelating agent, such that the acid at least partially spends as the pH of the treatment fluid rises; and complexing a metal ion with the chelating agent once the pH of the treatment fluid rises above a pKa value for one or more of the carboxylic or phosphonic acid groups of the N-(phosphonomethyl)iminodiacetic acid.