Yes, it all depends on how high you are compared to the diameter of the horizon circle.

The problem with the hola-loop is the diameter is so small (and fixed) compared to you, and its diameter never change according to you moving it up and down. In the oblate spherical planet, such diameter changes according to your altitude, to a certain point.

Think with me: If you are floating on the open high sea, you can not see very far, your horizon is limited by the 8"/mile, and most of all, the waves and turbulence in the water, but imagine you stand at 30 ft high, and can see far because you can see over the waves and turbulence. Even so, your horizon view distance is limited by the 8"/mile, maybe not considering waves of moisture affecting refraction of light, you will be able to see 3 to 4 miles, so that is the radius of your hola-loop. If you fly up to 300 ft, your hola-loop horizon radius will increase, keep the flat horizon line straight. Fly up to 10km high, hola-loop becomes bigger, still flat horizon. The only altitude your hola-loop stop increasing radius, is when the horizon increase can not keep up with your height, the curvature escaped in an bigger angle than your distance (altitude) can not see it, and that is when you start to see the curvature of the horizon as you stated, yes, it happens, I agree with you, but only in altitude proportional to the diameter of the hola-loop. In case of the Earth, the diameter is big, you need to be far away for that to happen. See, I agree with you, it is just a matter of proportions.

I don't have a graphic generator software here, tonight I will post some nice drawing about mending 4 "pictures" of 90° aperture to make a panoramic view of 360°, even with small degrees of curvature down on the edges, the final image becomes what you do not see in real life. It will be a dented horizon, you don't see it when turning your head on open seas, not real.

There is a visual misconception about what is up/down, front/back on our world observation.

If you see a hola-loop in the ground, and you are standing up one meter outside it, you could state that in a 2D representation the farther side of the loop is high, the closer side is down, it appears like that in a photo, right? But your intelligence tells you the hola-loop is flat on the ground, so it is leveled horizontally, no up, no down, just a visual interpretation of the 2D observation. You can even swear that loop forms a curvature, yes, but horizontal one, over the ground.

Now, imagine 100 hola-loops each one with an increasing diameter as a function of sine(), if you pile up those loops you will have one half of a ball (hemisphere), number those loops from 1 to 100, being 1 the small on top, the largest (100) touching the floor. Now, if the diameter of the #100 is 10 thousand times bigger than you, and you are over the #1, maybe you could see the #1 and #2, being the horizon. If you go higher vertically, start to see the #3, #4 and so on, perhaps very high you could see #50, much higher, #70, astonishing higher, perhaps #99 or even #100. What curvature would you see, even when seeing the #100? The curvature of the loop, you can not see the curvature made by the sequence #1 to #100, you can not, you are on vertical top, you only see concentric circles. Of course, 3D image can show you the #100 is further down than #1, but you still "not seeing any curvature", only the curve (circle) of each loop in the pile. Well, the curvature of each loop is a nice proof of the hemisphere being curved, but that is horizontally curved, not vertically. To see it vertically, you need to move yourself down and out of the top, go horizontally far, at height of loop #50, then maybe you will see the hemisphere sideways, curved vertically.

We are talking the same thing, just a matter of proportions and what curvature you are trying to show, the horizon circle curvature or the vertical curvature made from you to distance? That is the one people try to prove showing boats disappearing below the horizon. You can not capture that curvature horizontally in front of you with a photo picture.