You are not supposed to mess with the top and bottom areas of the frame. Believe it or not, that is where all the strength is. If you notice, all official gooseneck hitches you buy fasten to the vertical sides of the frame. That being said, my truck had this exact same type of homemade hitch welded to it also. I have never had a problem with it. I just got finished putting a dump bed on it, and had to cut that hitch out. Being afraid like you, I just took the torch and cut the center out, and left their welded on part on the top of the frame and did not bother it.
You can do a google search, and you will see all the big truck companies have rules about modifying their frames. You can weld and modify the frame, but there are certain ways to do it, and they usually want you to stay away from the top and bottom short areas, and only drill and weld to the vertical piece. I noticed on a 1989 f350 cab and chassis frame, Ford had welded a narrow piece of metal to the top and bottom of the horizontal areas of the frame to beef it up.
Yeah I've seen a lot of that and that's what makes me nervous. I think I'm probably going to end up lightly plating the underside of the worn area and just filling the top with epoxy prior to paint.