If the solar system is nearly flat, then why don't all the planets appear to lie on the same axis when viewed from earth? For instance, consider the image below. The location of the planets seem to be so random relative to Earth. If the solar system was indeed flat, then I would expect the planets to lie on the same 'plane', and relative to us, it would look something like the second image. I mean, maybe Jupiter and Mars and Saturn could be on the same plane, but I fail to see how Venus would be.
What is wrong with my understanding here?
The first image is from a July article by TV meteorologist Brent Watts.
Approximating that view in Stellarium:

The yellow arc is the ecliptic, the plane of the Earth's orbit around the Sun.
It looks curved due to the map projection.
If the view is centered on it, the ecliptic looks straight:

Unlike the Sun, which appears on the ecliptic at all times, the planets can appear a few degrees north or south of it because their orbital inclinations are all slightly different.
The more another planet's orbit is inclined relative to ours, and the closer it approaches us, the more its ecliptic latitude varies.