You know why you're wrong though??? Because the horizon always remains at eye level no matter how high you go, which is not possible on a ball. On a ball the higher you go, the LOWER the horizon gets. Just because you're on a flat surface doesn't mean you can't see infinitely, even with a telescope, UNLESS you go higher vertically.
1,601 feet though..... Right.
You are seriously confused and are not fully grasping the subject...
I think the fact that you think the horizon is something on the ground is sort of confusing you the most... In actuality ground horizons are a poor representation of horizons, because you have the earth obscuring almost half of line of site..
I think a much better example would be looking up and picking out the furthest start you can see in the sky..
Now the horizon is based on what you are looking at, not an actual object..
So if the star I am looking at is the hightest thing directly above me, then from there you can create your imaginary lined and have it converge on that star..
now the further away that star goes, the smaller it scales and the closer it comes the larger it appears to be getting..
The key to understanding what going on, is knowing that as long as this star is in your live of view, the only way you would stop seeing it is if something gets in between you and the object..
In space there are tiny particles, our atmosphere, and light pollution that can interfere or get in the way of the star...
however if you were in space like the Hubble Telescope or in Hawaii at the Mauna Kea Observatorie, that sits 4,200 meters high then a lot of those obstructions would be greatly reduced allowing you to see a lot more clearer..
And with out obstruction any object that is above your obstruction will remain above it, any that below will remain below...
On earth its the same as viewing a distant star, only difference you have the ground obstructing half of what you see, you cannot see anything below the ground because the ground is resting on top of it..
However like in space any thing above the ground will always remain above the ground and anything below will remain below it (unless it starts to move)... And going back to our original rule, things will always be visible unless there are obstructions to get in its path, so in theory a object that is above the ground in a infinate plane will always remain above it, and as long as it is above the ground it should always be in view..
Of course we know the earth is round and not some computer infinite plane simulator , in the real world far objects will start to become blocked by the curvature of the planet... And the way it happens is the obstruction starts from the bottom to the top exactly the way you shown in your picture..