I think that the American people greatly connect with this portion of SNL because they see performers out of their usual element trying something new (most of the time), and because of that see themselves as equals with the host. The monologue takes the "glow" off of a star, and for a few minutes they are just like us; this is usually seen in any awkward moments that occur during their speech. This reflects the American Dream in that all of us want to be the best. In the moments where our Hollywood stars are mere "humans" like us, we can see ourselves as their equals and experience pure bliss.
Another aspect of the SNL monologue that is appealing to audiences is the fact that it is a break from the routine skits that the permanent cast members perform. It is a chance for the host to showcase their own comedic abilities and have their own personality involved. While some of the skits in SNL can involve aspects of the host's life, the monologue is a time where they have the stage completely to themselves and can share with the audience whatever they like. This change of pace is appreciated by the American audience which often gets fed up with repetition. Also, the audience gets a chance to hear the latest news regarding the host's life.
The monologue starts off every episode of Saturday Night Live, and this monologue has now started off my blog. In the same way that SNL's monologue is a chance for viewers to see the host by themselves, this monologue too has been a chance for me to show you what my writing is like and what this blog will be like. Hopefully you have enjoyed it and will read the rest of my posts.
-Peter