being from suburbia and clueless about tractors, could you explain why the hitch is mounted at 3 moveable points on the tractor?
That is a good question. The simplest answer is that you must be able to lift and lower the implements so the points must be able to rotate. There is more.
With a 3 point hitch the implement behind the tractor can be adjusted to engage the ground at the most optimum angle, pitch, or height. The hitch will hold the implement at the position the operator drops or adjusts it to. Each arm can be adjusted to get the best use of each of the 3 pt tools. There are literally dozens(hundreds) of different kinds of 3 pt implements. Your hitch needs to be able to be easily use all kinds and that is why the points are moveable.
3 pt hitches were way more easy and versatile to use than a simple hitch or two point connection from several decades ago. It became the industry standard for tractors and universality of implements. To the unpracticed it is still a difficult and injurious way to attach tractor implements. 3 pt hitches are PITA, but changing the industry standard now is cost prohibitive. Several new items are on the market that make it easier to attach an implement to the hitch.