But if perspective is the only factor involved, objects will only meet the horizon at infinite distance. We know it can't just be waves obscuring distant objects because we know the theoretical horizon, and distant objects sink below it.
Nothing meets the "horizon." It just appears to. Anyone that told you otherwise clearly misunderstood.
I still don't understand why you think, on a sphere, that you would be able to easily see the curvature of the earth in the distance but curvature on the horizon would be barely detectable at 50,000 feet in the air.
It would seem we live on a cylinder if that is the case. Pick up a roll of toilet paper if you want to see a handy example of a 3D object in which you can see the "edge," or curvature along one axis and not the other. Or, pick up a ball and try to see curvature along one axis and not the other on a sphere.
Point being. The horizon is not the curvature, on a flat or round earth. It is still just the distance in which your eyes can resolve a subject to the laws of perspective.
I know this is late, but I hope it's better late than never. I made a reply to you in
Flat Earth Debate / Re: Horizon. I hope you find it helpful. Some of the material there is relevant to the answer to this post.
I don't follow how you can state categorically "Nothing meets the 'horizon.' It just appears to. Anyone that told you otherwise clearly misunderstood."
Again this explanation applies to the Globe.
To explain why we do not see "curvature along the horizon", but do see its effects in the direction moving away from us,
just imagine you are on a tiny island in the middle of the ocean with your eyes an arbitrary 5 m above the ocean (nice and calm too!).
As you look all around, the horizon is exactly the same distance from you and would be about 8 km away, with a "dip angle" of a tiny 0.07°. In other words all around the horizon looks at the same level, though it is actually about 10 m below you eye-level. So, if the horizon is the same distance below you eye, there is no "curvature" to be seen. Though the horizon will look like a circle around you, but at the same level all around.
But, when a ship sailing away from you reaches 8 km it will appear "on the horizon" and any further away will start to be hidden by the horizon.
Even at 1000 m elevation (some tiny island with a 1000 m tower!) the same thing applies, the only difference being that the horizon distance will be about 113 km (more if we have typical refraction) and the horizon will be 1.0° below our eye-level. This is still not enough "dip" to be noliceable, or for the circle of the horizon around us to show noticeable curvature. Even if it did, the field of view of a standard 50 mm camera lens at 113 km would be about only about 20 km each side of the axis. The "curvature" in this would only be about 30 m (I am hurrying, so could make misteaks!). This (30/20,000) would not be measurable. In any case I don see it as existing at all.
But, this is the reason that "curvature" going away from us IS very noticeable (objects like ships, buildings and mountains can be hidden by it, while "side-to-side" curvature is a few metres in 10's of km, so simply would not show.
Now, let's get up real high, say 20,000 m. Again the horizon is the same all around us, but is now about 4.5° below the true horizontal. This IS starting to get noticeable to the naked eye. I have never been to that altitude, but reports from Concorde passengers and crew are that the "curvature" can be seen.
The horizon would still look like a flat circle below, but noticeably below eye-level - in other words, it would be a bit like looking down on a large disk. On the globe that disk would have a radius of about 500 km.
This is where many Flat Earth supporters also accept that we see a disk below us - they claim the disk is the "disk of the earth illuminated by the sun". Of course I don't go with that explanation, but I suppose it is an out if you really don't like the Globe. Even a 1,000 mile diameter chunk of the Globe would not look that curved from above.
I should have thought this out better, but this is all the time I can spend. I hope it's not completely wasted.