You should only write out a speech if you have something important to say and you want people to take it and you seriously.
If, on the other hand, you don’t have much to say,
if you don’t have a strong opinion one way or the other,
if you don’t have time to gather supporting evidence and to link it together in a clear and logical way,
if you have more important concerns to attend to (e.g. going to one more meeting or catching up on your email),
if you’re an accomplished speaker and you think you can wing it or speak from a list of talking points someone else developed,
if you’re so important that you don’t care what people think about what you say,
if you don’t have or won’t make the time that’s required to write out a speech (or to meet with a speechwriter),
then by all means don’t write out your speech.
Can you get by if you simply outline your speech and speak extemporaneously? Possibly, but only if you’re articulate, experienced, and uber-confident in front of an audience. And is that what you want to do, “get by”?
To create a speech that stirs people’s hearts and minds, lingers in their memories, and rouses them to action, you have to write it out.