I have been thinking about this question for a few days now. IMO it comes down to an individual's character, theme, style and/or persona. Like the magic wand, people see magic words as a classic icon or emblem of the magician. Magic words are of course used all the time by Harry Potter and friends (e.g. "Wingardiam Leviosa" or "Expecto Patronum"). But that fits the theme, and those are specific spells to bring about specific results by those playing the part of being able to do real magic.
Now it would look pretty silly for say, David Blane, or a sophisticated exponent of gambling routines, and perhaps various other stylists, to say magic words. I did it when I used to dress up and perform as Merlin and it went over very well. People loved the Merlin persona, and expected a wand and magic words.
It can also be great when performing for kids, especially really young ones, because kids live in their imaginations and are more apt to indulge in the fantasy side of the magic.
Finally, it can be done as tongue in cheek comedy, if that suits your style. e.g., "Now we say the magic words: I hope this works," "We just say the Catholic magic word - BINGO," or even David Williamson's gag: "Now we say the magic words -- The magic words."
Robert Houdin wrote centuries ago: "A magician is an actor playing the part of a magician." So, in some ways, it comes down to what kind of actor one wants to be. And that's a huge part of the fun of it all...