Coffee would be ho’etz if one were eating the coffee itself. It’s only shehakol because one throws out the coffee after cooking it, and one drinks the water, which is halachically considered not to contain any of the coffee’s substance (ta’am ein bo mamosh).
Which leads me to consider the odd question of what exactly is in a jar of instant coffee. It is simply the “ta’am” that was infused into the water when it was brewed, so if halocho considers it not to exist then the jar must be empty! And if it doesn’t exist then how can there be a problem with cooking it on shabbos?