Though Mark1 has a point, it's not quite as absolute as that. I believe that Lake Country will conditionally rent solo.
Consider that it's not so much the cost to insure the inexperienced floatplane pilot because of the plane itself, but rather the much more variable conditions into which that pilot could land the plane, and places, (which are very certainly not airports), where the plane could be left stranded. The skill to fly the plane is reasonably basic, it's knowing where to NOT try to land or takeoff, which requires the experience. Therefore, as long as the trained pilot is mentored to land at only selected places for their early stages, it can be safely done.
Another amusing problem is that you can fly over an appealing lake, check it out, and land into it perfectly fine. But then when you plan your takeoff, that arm or bay which looked long enough from above, now really does not. It is surprisingly easy to get "lost" on the lake you just landed on, in that you can't figure out where the best departure path is. Often where you land, and where you takeoff will not be the same place on the lake.
A lake I was trained in decades ago in a C 180, was "S" shaped, such that when you started your takeoff run, you could not see the part of the lake where you'd leave the water, it was around the corner. And, that lake was only 1300 feet long. I flew over it in the amphibian last summer, and shuddered at the thought of trying to takeoff in there! Perhaps the wisdom of age!