The thing with a DNI is that, depending on how advanced it is and how it's implemented, can take a couple of steps out of the 'normal' process.
Reading: My eyes catch the light and bounce it on those stripes and cones (or whatever it's called in English) in the back of my eyes, with then send it to a part of my brain which makes an image out of it. That image is transfered to another part of my brain which turns that image into text, that text is then sent to a part of my brain which interprets that text, which then also has to take additional steps to translate it because it's not my native language.
A DNI might be able to skip part of that process and immediately send messages directly into the language-part of my brain, skipping past several of the interpretation steps which take place when reading this forum.
And, another thing: Speaking a 3 second line doesn't to take up 3 seconds of actions for the simple reason that, unless you've got some kind of attention disorder, it's fairly easy for a person to work with his hands, legs and rest of his body at full speed while talking.
Ingame, this works by simply making talking a free action. That way, you don't do: 3 second action: Speak: "I am reloading, cover me!", 1 second: Eject magazine, 1 second: take new mag, 1 second: slam into gun, arm."
Instead, the three seconds of talking overlap the 3 seconds of action taking place.
(This is just an illustration for the overlap function of speaking as a free action, actual RAW actions are slightly different.)