For corn, I would agree, if it is time just plant at your standard seed depth. I really don't like corn in a trench for several reasons. When it rains it will emerge. Maybe plant a little bit deeper (2") than usual.

When planting beans however I would take the other approach. Beans want to be planted shallow but into moisture.  This is where unit mounted fixed/non floating row cleaners come in.

When planting beans, screw your row cleaners down to move enough soil out of the way to get them into moisture but only 1/2-3/4" deep. Yes they will look like they are in a trench but they will likely be up and growing in a few days.

With beans you want to get them up and out of the ground as quickly as possible. When its dry your choices with beans are either plant them 5" deep and pray they make it to the surface or plant them 1/2 inch deep and pray for rain.

I prefer to plant them into moisture but move most of the dry soil on top out of the way so they are actually only 1/2" deep but in moisture.  The trench and mound between the rows (I am talking about 30" beans here) will mostly level out over the summer but yes, you will have some low beans tough to harvest. But at least you will have a crop. And it could be a good one. jmho.

Good luck.

Jim at Dawn