Ahhhh, a very good question and one I will answer with one caveat, it is my theory because there is no proof or historical record to truly answer this question. Here is what I believe:
The collection of kata we are required to learn in modern martial arts didn't begin until the mid to late 1900's. In the 1600's to the 1800's karate was actually referred to on Okinawa as "Ti (pronounced like tea)." This indigenous system was separated by distance between villages such as Naha, Shuri and Tomari. It may have been even more exclusive to smaller villages but as of the 1800's these villages were known and promoted in the 1900's as the three main factions of Ti.
Those Ti masters or experts tended to teach and "know" one, two or maybe three kata. We all have heard the legends that those elders tended to require several years to learn and master one kata. The stories or legends even stated in one system the kata that is known today as "sanchin" is the first kata that must be mastered and that it took three (guessing the time window here) years to master. I imagine this is how the question came into being.
Why indeed, does it take several years to master one kata? It comes down to an attempt to understand what comprised that one kata in those years before the mass effort to bring karate into the school systems per WWII needs of Japan, maybe even earlier. Before Ti came to the lower classes of Okinawa the exclusivity of practice, training and applications were held close to those who practiced. It might even explain why such traditional requirements as "introductions" or "recommendations" were required to even get a chance to learn the system of some Ti master.
Then you have to understand some of the teachings that may have been withheld from the Western mind either by the intention of the master teaching the military or by exclusion as things transcended from the ancient traditional methods to more modern methods of a school system, etc. Things were toned down and many intricacies were removed to ease the learning processes of young adults in the school systems.
In addition the traditional method of learning a martial art as explained by the levels of "shu," "ha," and "ri" dictate that what is and was introduced and taught to those young adults was true to this model or method, the strict lessons of the level "shu." Because of the difficult and tumultuous situations of war and other influences of being a country concurred by first the Chinese and then by the Japanese in the 1600's the levels of "ha and ri" were lost and/or forgotten except by the masters who many we lost when they died during the war.
To attain a level of "ha" and "ri" requires that the practitioner learn much more than the mere basics but the actual principles that are the foundation of all martial systems. This is how we begin to learn the need to study one kata for a length of time as told in the legendary stories of Ti practitioners of Okinawa.
Principles are many, although limited by the fact that they are finite principles due to physics, etc., and to learn them each and then to bring them into a "one whole and holistic" practice takes a lot of time. In addition to learn and apply kata and its technique(s) means you don't just learn the patterns but each and every individual nuance of each technique and combination derived from kata practice. To achieve a "ha and ri" level requires the ability to instinctually apply not only the obvious kata application but the nuances underneath them as a separate and unique entity so that the mind and body along with spirit can apply any principle instinctually and in the moment as needed by that moment to work.
Try taking your first kata and mixing, matching and modifying according to any given situation even in training with the other more theoretical and philosophical principles being applied. Losing the pattern and rhythm of a set kata is difficult without first coming to know, understand and apply each minute atomistic quality of said kata from any direction or dimension according to the fluidity of any given moment. This takes a lot of work and only a few will actually make the effort necessary to reach these levels while others accept today's rendition of karate or Ti in a sport oriented fashion where kata are dances and fighting abilities are reduced to who can "tag" another target for a "point."
This does not even take into consideration how today's martial systems are encumbered by societies "rules and requirements." To achieve a level of understanding and application means opening the mind and leaving the rules in the dressing room. Not many can achieve this in today's litigious societies or if you prefer today's commercialized societies.
It does take several years to truly master one kata when you apply "ALL" the requirements but to achieve the level of "shu" that is merely a ghost of a system it doesn't take much and there lies the reasoning behind learning many kata, many systems and achieving many levels of many systems of black belt status.
Then again, all this is my theory as to why it takes much time, effort, sweat, blood and tears to learn just one kata. Who is up to the challenge?