In engineering terms, three-point attachment is the simplest and the only statically determinate way of rigidly joining two bodies.
The primary benefit of the three-point hitch system is to transfer the weight and resistance of an implement to the drive wheels of the tractor.
The N variations are common in "quick hitches" and allow larger tractors to easily hook onto smaller utility implements.
The main reason why this was the default hitching idea is that it was the natural follow-on from the days of horse-drawn implements, which were towed as trailers by the horse or team (and often had an operator's seat).
Towing with a drawbar is a good, practical system for many purposes, and it has continued to be used even up to today, but the three-point hitch outperforms it in several ways (described below).
During the decade of 1916 to 1926 he developed his ideas through various iterations, duplex and triplex, mechanical and hydraulic, to arrive at the patented form.
During the next decade, he continued explaining and selling his hitches and implements and even produced his own model of tractor in cooperation with David Brown Ltd. via the Ferguson-Brown Company.
In addition, the three-point hitch would prevent the tractor from flipping backwards on the drive wheels if the implement being dragged were to hit a rock or other immovable obstruction.
Ferguson and his colleagues developed several innovations to this device (e.g., the hydraulic lift and depth control) which made the system workable, effective, and desirable.
During the 1940s, it was so advantageous and popular that other manufacturers were compelled to come up with competing hitch improvements that could also be pitched as proprietary "systems" with at least some of the features of the Ferguson system (such as quick, easy hitching and unhitching, implement raising and lowering controlled from the tractor seat, and treating the tractor and implement as a unit rather than an articulated pair).
Likewise, JI Case developed its Eagle Hitch, and similar path was followed at John Deere.
They also presented the problem of incompatibility between brands of tractors and implements, applying pressure toward vendor lock-in that many farmers resented.