I think intros and outros are important for multiple reasons, however it depends on the style of video you are making.
Take gaming as an example (because it is over saturated as a market and easier to explain.
If you are making a video that is fast paced and you want to get the viewer right into the action, leave the intro out but include an outro. If you are making a slow paced, calm video then include and intro and an outro. Or if it is a fast paced video you can include a fast paced intro, with a max of 6-8 seconds. It all boils down to personal preference.
It is one of those things that it comes down to an individual video and your aim in the production side of things. How your intro is paced will set up the expected paced for the rest of the video.
You would not have a short, fast paced intro if you are doing a gameplay of Sims 3.
Equally, you would not have a long intro if you had a 1 minute Call of Duty kill clip.
Hope this helps somebody.