For outdoor HDRIs, the horizon line will be at the vertical center probably for all HDRs that you come across, unless the panorama was taken really high up which is improbable.
For indoor HDRIs, dome mapping really makes sense since light sources and objects will be closer to the camera and will make a difference when rendered from the correct vs incorrect height. Even using a wrong camera height can be interesting sometimes.
Dome mapping is preferable too when you render an object on a surface that uses the HDRIs projection on the ground with a shadow catcher for example . Anything close to the surface will look definitely better as there's quite some difference between how the surroundings look to an object at 0.1m vs 1.6m.
In order to determine a somewhat correct height at which the cam was placed you'll need to know the physical scale of a feature visible the pano, best one that's on the ground. It can be anything like street markings, a tile, a curb, something that you know to some certainty, the bigger the object/feature the better.
Create a plane at 0/0/0 big enough to cover the ground of your HDRI and assign to it an UVW modifier in spherical mode.
Create a material for the plane, assign the HDRI in question to it and display it in the viewport.
Once you have the plane display the HDRI on it, you can move the UVW mod's gizmo up/down and see how the projection/mapping of the HDRI on the plane changes. You might have to increase the plane's tesselation for a better result in the viewport.
Now create an object similar in size to the feature in the HDRI and place it somewhere where the feature is projected on the plane. If you move the gizmo and the feature projected/displayed on the plane and the object you created match in size then read what the Z value for the UVW mod's gizmo says - that's roughly the height the pano was taken at.
I'm saying 'roughly' because the method is not accurate. Accuracy will improve with increasing size of the feature though, that's why it's important not to use small objects as features. It will also work only somewhat reliably on the things that are on the ground closer to the camera. The farther the object from the camera the more it gets distorted when projected on the plane, making it hard to determine the correct height.
Still, this method can work surprisingly well since it 'maps' the surroundings on a plane and helps to get an idea of its physical scale. Once you have some other 3d geometry in the scene to compare the projected HDRI's feature to, you quickly see whether the scale (or better projection center / UVW mod's gizmo) is far off or not.
Note - I'm not in front of the PC right now so can't check - I've done this a lot in the past but can't remember if I used camera projection or spherical projection from a UVW modifier on the plane. I know one of these methods had an advantage because it works better in the viewports. If the above method doesnt work for you, let me know so I can check.
