The stupid thing about all this is the reality if we did live on a flat earth is the horizon would still not be at eye level.
If I amend your diagram to show a flat plane instead of a curve and we agree that you can only see a finite distance then you'd still be looking down to as far as you can see:
Except the flat earth contention is that the ground plane appears to rise to eye level. So even looking straight ahead (no angle downward), the horizon is at eye level.
This is the vanishing point argument. If you look straight ahead, that's where that particular ocular vanishing point is. If you look up, that's another vanishing point. But straight ahead, due to perspective, the vanishing point appears on the horizon.
And that's a convention oft repeated in art direction. The horizon is the straight-ahead vanishing point. Squat down? Still on the horizon. Stand up? Horizon. 3rd story of the Grand Brighton? VP still on the horizon.
It works for everyday situations when your perspective is relatively near the ground.
But what I don't see is anyway to calculate such a distance as if it's anything actually empirical and not just a principle. That's why I call such a horizon "apparent." It depends on visual acuity, resolution, focal length, etc. And even then, is it anything more than subjective?
The horizon on a curved surface is something real. It's a quantifiable distance that factors height and radius of the sphere to know where that tangent line is. It's not "apparent."
I've kind of stopped worrying about how an art/drawing principle of capturing a 3D space on a 2D medium can be applied to understanding physical space. So the ground appears to rise and the sky appears to descend, FE says. So what? If that's what flat earth believes, I'm not going to change minds.
But it ought to be measurably verifiable whether or not a horizon is always level with the eye. It's not proving to be so, so even if it were an attribute of a flat plane perspective, it definitely is not one in space with spherical geometry. So, it seems reasonable to me that if it's a discriminator between flat and spherical, it ought to settle the matter. And I think anyone could check, as long as it's not done sloppily, which is how Rowbotham's experiment seems to have been accomplished. But you don't need a government agency or MIT team to verify. You don't need expensive equipment.
If the horizon DOES always measure to be level to the eye (not appear; be measurable on the horizontal), then it refutes the globe. If it doesn't, then that's a big point in globe's favor and maybe then flat earth proponents will abandon the vanishing point argument.