You could do multiple channels, but I think if you really, really want to capture the "I'm watching this with the rest of the country" feeling, a single live channel would be the safest bet.
It also may have value strategically, because there are some shows that "work" more as a live show, and there are some TV series that have better cultural impact if they are released in a serialized way. For instance I suspect Game Of Thrones has been more successful at permeating culture by releasing one episode a week than it would have been had the whole season been dumped at once.
Financially though, it's not clear this would work for Netflix. Now, depending upon how they pay for a given piece of content, they're paying for a lot of programming being used as background noise. You'd have to get enough people buying Netflix subscriptions because of this added option to offset the higher costs.
There'd be a "cable-style-menu" option to mimic the way cable / satellite menus have looked since the late 90's. Maybe 50 or so channels of similar programming running on a time schedule, where you have the option of catching the last 30 minutes of "Terminator 2 - Judgement Day" or watching from the beginning.
Its mindless, but I think that style of consumption is what a lot of people want. It to do the hard work for them.