What's realistic isn't necessarily what makes for good television. I agree they probably should have had characters who specialized in away team missions that didn't necessarily consist of the bridge crew.
But I disagree that it's a huge risk to take your bridge crew off the ship. Besides the fact that given dramatic license they don't expect that something will always go wrong within ten minutes of arriving anywhere, just because somebody doesn't have three pips on their collar does not mean they are not qualified to run the bridge. There are plenty of very competent lieutenants on the ship.
It's usually referenced that they do full scans of the surface before landing anywhere, but they're on an exploration mission, not a survey mission. They want to experience what's on the planet, not just note it down in a journal.