It's funny logic, but in reality you're wrong. You only need a seaplane qualification to operate in and out of the water. So yes, you can fly an amphibious aircraft on the ground with an ASEL certificate. Most private pilots will choose to obtain a single-engine land-based pilot license before applying for a single-engine seaplane license as an additional qualification.
To earn a seaplane qualification, you must demonstrate your competence. There is no established experience level for the qualification. You can add a seaplane rating to your certificate in as little as 2 days. Usually, you'll complete around 5 hours of flight training followed by a check-in.
I recently got my qualification and I promise it's one of the best experiences you can have as a pilot. Most people who earn a seaplane qualification will tell you that flying and getting a pilot qualification were the most fun they've ever had in their lives. Every landing and takeoff you make on a seaplane will be different. Unlike ground flight, where most pilots operate on smooth, long and unobstructed paved surfaces, landing in water is quite a challenge.
However, landings in crystal clear water are actually the most dangerous maneuver you can perform as a seaplane pilot. As for cross-country flights, it's known that a C150 can fly and stay still as it travels from point A to point B. If you ever see a white and yellow beacon turning (instead of white and green), it's a seaplane port.
