The wake behind a ship spreads out behind it. This is easily demonstrated with a toy boat in a bathtub. The wake isn't a straight line into the horizon.
Yes, the white water wakes do widen with distance, but nowhere near as fast as the bow-wave does.
There have been studies on it and while it varies a bit with wind direction, typically it varies fairly slowly and might be be
100 m wide 1000 m from the ship, and
180 m wide 6000 m from the ship.
These figures are from 100s of actual measurements on a very large cruise ship, though not the P & O one in the photo.
But, the only inference I made from the wake photo was that was not zero width at the visible horizon.
How about simply posting an appropriate example rather than waves behind a ship?
Not quite what you are asking for but:
To me at least that looks like a sailing boat closer than the visible horizon and buildings well behind the visible horizon. Again, in my humble opinion of course, that demonstrates that the visible horizon is not the "vanishing point".
Again:
Likewise, to me, that seems to be a sailing ship at the same distance as the visible horizon ("on" the horizon), and clearly is not yet at the vanishing point.
This one shows the Suez Canal going to the horizon. I would rather have had one taken with a normal lens and not a wide angle like this - any appearance of curvature is the camera!
From - Timelapse of Adrian Mærsk sailing down the expanded Suez Canal There are undoubtedly better examples, but the visible horizon need not be the vanishing point, in fact to me the "vanishing point" is an aid to drawing, not a "physical point". Small objects seem to vanish in quite a short distance. If the resolution of the human eye is about 1' of arc (as I believe the Wiki says) the vanishing distances would be about:
4 miles for a person,
65 miles for a sailing ship with 100' masts
130 miles for the 200' width of New Suez canal (but with the quality of that photo and lack of contrast, I doubt it would be that far) and
650 miles for a 1000' building.
So, we would not expect the visible horizon to be the "vanishing point".