My dishwasher is not draining properly and while taking a look at things I realized that the drain hose is not tied into the garbage disposal. Is this incorrect? Are there certain benefits for having it this way?
I would say that failure to drain would be an internal fault in the dishwasher and nothing to do with the type of drain present. This is the first time I have seen a reference to a separate drain for a dishwasher. Could it be that this separate drain was originally for a clothes washer?
Disposers have a port for connection of dishwater waste water. I have always thought that this was for the convenience of not having to separately plumb a dishwasher into the drain above the trap. There are tailpieces with a side arm to accept the dishwasher waste and these are the standard connection if there is no disposer.
It is recommended to connect the dishwasher discharge drain into the disposal for this very reason. Food will eventually get trapped in the dishwasher drain when it does you experienced this problem of your dishwasher not working properly. However if you were to connect the dishwasher discharge drain directly to the disposal and loop the hose high up underneath the counter and experienced a blockage it wouldn't go back down to your dishwasher, but it it would land in the disposal.