I understand this desire.
I think there is an ancillary problem in time travel that is not really considered. Not only would it be neccessary to unwind all the events that happened in the past, but also precisely locating your self spacially in that river so that you end up in the correct time, but also in the precise position in space. You want to end up at the door of some bookies office to bet against the Chiefs winning the Superbowl in 2024, not accidentally 200 feet over the surface of earth over his office in Las Vegas, say, falling to your death, or, worse, having your machine land in the correct time, but a lunar distance from blue earth as you rapidly expire from exposure in the vacuum of interplanetary space.
Yup. Ages ago I saw a large well-attended talk by J. Allen Hynek, and he went over three possibilities for unidentifieds — terrestrial (basically, either classified vehicles or foreign powers), extraterrestrial, and “metaterrestrial”. The third one was that the visitors are from our own future. But of course, same problem applies as you just spelled out. It doesn’t solve the distance problem because in addition to the tiny little problem of time travel, one would also have to span great distances. :^)