in my opinion straight on flat bars aren't designed for intended for long "steady state" cycling. They're designed for mountain biking which has frequently changing terrain, body position, etc.
Look at the way your hands sit on a flat handle bar. The knuckles are perpendicular to the arms, and most likely your wrists are cocked. Finally, there's absolutely no chance for variety in hand / wrist position. Then look at how your hands hang in a neutral position, for instance when they're hanging at your sides. The wrists are relaxed and neutral (not cocked) and your knuckles are pretty much 90 degrees from their position on a flat handlebar.
Your hands, arms get numb and your shoulders and neck get ****zed out because your whole body is forced into a position which isn't natural, which doesn't allow variation and on a ride which the bar isn't intended for!
SOme people can tolerate this mismatch between bar and purpose better than others. If I ride my mountain bike on the road, I'm not having fun within about 30 minutes.
Road bike bars are not made as torture devices as many who just aren't familiar with using them think. They are intended to allow a wide variety of hand positions including at least three that allow the hands and wrists to be in a neutral position with relaxed neutral wrists and the knuckles in the same position as when relaxed at your sides (the three are on the "ramps", on the hoods and on the drops).
Either get some road bars for long distance riding or explore the alternatives mentioned above. These are the sort of bars actually designed for the riding you want to do.