Smartphone vs camcorder
There are a few things you are missing, and a few more you just aren't fully appreciating how much of a difference the things you mentioned make.

First, the S6 sensor is not over 1/2 inch, it is 1/2.6 inch, which is substantially smaller than a 1/2 inch sensor, particularly since sensors are measured diagonally.  

Second, lenses matter a lot more than the sensor.  The inability to zoom optically is a deal breaker for what you are trying to do with covering speaking events.  Typically, video is a secondary concern to a live audience and camera positions will be far off to avoid impacting visibility.  Without strong optics, you will not be able to get the footage you need.

Third, most (all?) cellphones do not use a global shutter, while most camcorders do.  Global shutters ensure that an entire frame is captured at the same time instead of scanning line by line while the frame is exposing.  The lack of a global shutter results in the "jello" effect that you can see when you pan a camera quickly.  Global shutter is a bit less of a concern for fixed camera position shooting at a relatively static target, but it is still work mentioning.

Forth, reliability.  Smartphones are more likely to crash than a stand alone video camera, they are subject to recording length limits that may interfere with your recordings.  They will have lower battery life while shooting which may also cause issues and the S6 in particular does not have a replaceable battery at all, so when you are out of juice, you are done unless you have an external battery pack that can keep up with sufficient juice.  Even then, it's a disadvantage to the much more compact battery placement directly on a camcorder.

Fifth, stability.  While you can get tripod mounts for a smartphone, camcorders are built from the ground up to support tripod mounting in a secure way.  You can work around that on the smart phone with complicated cases and mounting systems, but those also drive up the cost.  When shooting off a tripod, camcorders also still have a stability advantage.  You can hold them up to your eye and form a 3 point support that is easily held steady.  Accomplishing the same with a phone would require expensive rigging running up in to hundreds or possibly over $1000 unless you want to try to do custom fabrication yourself.

There are probably a few other things I'm missing too as I've just been writing these from what has come to mind as I go.  Smartphones are up to the point where they can make a pretty decent (though less durable and more expensive) alternative to a go pro, but they are really not an alternative for a camcorder by any stretch of the imagination.