You're describing my first moped: https://www.mobylette-mag.fr/wp-content/uploads/2017/06/cara...
They don't make those anymore, but they were incredibly fun to ride (and at the time, it cost 6000FF new, which translates to maybe €1000-1500 today).
But just like you did, I kinda feel like cross country road trips would be excellent on back roads via motorcycles. In a car, it's a bit disconnected and insulated. On a bike, it just seems way too slow and tiresome.
Only things I'd want in a cross country motorcycle is: a machine that's under 50 pounds, has a max speed of 50 mph (I'd prefer to keep it at 20-30 mph), goes 300 miles per gallon, and costs under $3000. SO I GUESS I WON'T BE TAKING THAT CROSS COUNTRY MOTORCYCLE TRIP EVER THEN.