OK my $.02 as a sound guy and a bass player.
I'll most often DI a bass. Why? Because I'm lazy? No! Because the name of the art of doing what I do is "sound reinforcement". Often, the sound from the bass amp is boomy, muddy, and just plain bad when it gets to the middle of the room. I won't go into the physics of acoustics but y'all should research room nodes. So, what does the direct signal do? It allows me to add clarity to the sound that's coming from your amp. In other words, I take the (usually too loud) sound from your amp on stage and blend it with a nice clean bass signal to add some clarity back into the room.
Think of it this way, when you say a word you have the sound of your vocal chords making a very unrefined sound. What separates one word from another word is the shape of your mouth, what your tongue is doing, and the if you add ch's, th's, s's, k's etc... Those frequencies live in the 5,000 to 8,000 Hz range. Our ears have evolved to be sensitive to those frequencies because that's where words are formed.
So when you're playing your bass in ultra-rumble mode, I can't tell one note from the next 50 feet away. So I'll use your DI signal to add that 1,000 to 5,000 Hz into your signal to make your notes pop out.
That being said, if a bass player walks in with a pedalboard full of distortion boxes I'll usually toss a mic on the cabinet because DI distortion sounds nasty.
Now everyone tell me I'm doing it wrong.
Then go mix bands for a month or two and get back to me on that.