I'm just repeating, what I've seen out at sea:
The sticking point is the sharp "water-horizon-line".
With clear weather and good visibility, the horizon at sea is a sharp line. It looks like, as if your looking over some near mountain ridge and see other blurred mountains (sea, e.g. islands) behind it. This is all around you, all 360°. So on first sight, it looks like your sitting at the bottom of a very flat bowl. But as you proceed, the "bowl" is moving with you, you never reach the rim.
The only other geometry, which gives a similar view and can explain, that the view is sustained as you proceed, is the surface of a big sphere...
And don't try to explain this with "waves obscuring your view". I've been out in a storm, watching another yacht near by (less than a mile away). You clearly see the difference, when sometimes the yacht is obscured by waves so high, that you only see the higher part of the mast of the other yacht.