The Japanese did build some cheap carriers. Most were originally passenger liners before their conversion to carriers. Liners provided a reasonable starting point, since they provided a large hull with reasonably high speed. Some of the liners used had been designed with the intent to make them easy to convert to carriers (and their construction subsidised by the navy). One class of three planned ships (of which one was completed) were converted from tankers, and one carrier was converted from a cargo ship.

The four smallest of these converted carriers (the tanker and cargo ship conversions noted above, and the two smallest liner conversions) were not large enough to operate combat aircraft suitable for carrier warfare. Their flight decks were only a little over 100m long, too short to land combat aircraft such as fighters, dive bombers, or torpedo bombers. They could operate short-landing aircraft, such as the spotter aircraft Kokusai Ki-76 "Stella" (similar to the German Storch), and in principle the Kayaba Ka-1 autogyro (supply of these aircraft being the problem). Their typical complement was 8 Ki-76s, intended to support landing operations. Three of these ships were not pure carriers, but landing ships with flight decks - in addition to aircraft, they carried landing craft. Only the first of these 3 ships came into service before the Battle of Midway, so they had little opportunity for use as landing ships. They were used as aircraft ferries, taking aircraft to land bases (they could take off from the short flight deck, and didn't need to land), and were able to ferry 30 to 37 aircraft at a time. The two liner-conversion carrier-landing ships were sunk while in use as troopships, and the cargo-conversion one was completed at the end of March 1945 and survived the war without significant action. The tanker-conversion carrier was intended to provide air cover for convoys, for protection against submarines, but was sunk in harbour by air attack 3 weeks after being commissioned in 1945.

The five larger liner-conversions had a hanger (important for being able to keep the flight deck clear enough to land aircraft), and could operate 24 aircraft (except 1 which could operate 27). They lacked arrestor gear, which meant that they couldn't land aircraft quickly enough for carrier battles, so the operated as aircraft ferries and convoy escorts. Two were sunk by submarines while operating as convoy escorts, and two were sunk by submarines while operating as aircraft ferries. The fifth was sunk by air attack in harbour.

Each conversion generally took between 6 months and 1 year. More ships like these wouldn't have helped Japan in carrier battles. First, as they lacked arrestor gear and/or long enough flight decks, they couldn't operate aircraft usefully for carrier battles. Second, they were slow compared to fleet carriers, and this would have limited their ability to operate with such carriers. Third, the Japanese bottleneck wasn't the number of carriers, but adequately training enough pilots to replace the losses in carrier battles such as Coral Sea and the grinding attrition in the air battles in the Solomons. The Great Marianas Turkey Shoot demonstrated the futility of simply throwing large numbers of barely-trained unskilled pilots at powerful US carrier forces. Notably, in the Battle of Leyte Gulf, the Japanese used their carriers as bait to draw away the US fleet carriers (and most battleships), to give the Japanese battleships a chance to close with and sink the invasion fleet (the decoy carriers did their job well, but the Japanese battleships failed to make use of the opportunity to sink the invasion fleet).

Japan did need aircraft ferries and convoy escorts, so these ships performed useful service.

The five large converted carriers were the three Taiyō-class carriers (Taiyō, Unyō, Chūyō), Kaiyō, and Shin'yō (Shin'yō was converted from a German liner stranded in Japan by the outbreak of the war). The 3 landing ship-carriers were Akitsu Maru, Nigitsu Maru, and Kumano Maru (the last originally a cargo ship), and the tanker-conversion convoy escort was Yamashio Maru. These last four ships were owned by the Army rather than the Navy, explaining their more limited role and their names.

/u/wotan_weevil has done an excellent job discussing the wide variety of converted carriers, but I just want to expand on the points they raised in relation to why further carrier conversion would not have been beneficial to the Japanese in the Pacific War, as well as the limitations of what you're proposing.

As /u/wotan_weevil has pointed out, the major bottleneck the IJN faced wasn't necessarily the number of carriers they had available. In addition to the various conversions of civillian ships into the Hiyō and Taiyō classes of carriers, the IJN also launched several full sized fleet carriers. There was Taihō, a development of the Shōkaku class designs into a large armored carrier; the three completed carriers of the Unryū class, which were based of the design of Hiryū; and the Shinano, the converted hull of a Yamato class battleship, and the largest carrier ever built until the construction of the first US supercarriers nearly a decade later. Despite the construction of all these vessels, limitations on further development of improved aircraft, the lack of qualified pilots, and increasing fuel shortages meant that the IJN's air arm, that had already been ground down through the Solomon Islands Campaign, was completely shattered at the Battle of the Philippine Sea, never to recover.

Indeed, these kinds of shortages of aircraft and qualified pilots had dogged the IJN for nearly the entirety of the Pacific War. At the time of the Attack on Pearl Harbor, the IJN had barely enough of the Type 0 carrier fighter (the famous A6M "Zeke" or Zero) and qualified pilots of the same to fill its frontline units. The Kidō Butai had to scrape through nearly the entirety of the IJN to amass enough pilots and Type 0s to fill out their flight decks for the Pearl Harbor attack, and many of the second line Japanese carriers (smaller units like Ryūjō and Hōshō) and island garrisons were operating the older Type 96 (A5M "Claude") fighters. Even after the outbreak of the war, IJN air production struggled to keep up, such that--by the time of Midway--air strength on even the frontline Japanese carriers had begun to drop due to want of replacements. In fact, throughout all of 1942, the Japanese aircraft industry produced a mere 56 new carrier attack aircraft, hardly enough to replace the light losses experienced by the Japanese in their initial conquests, let alone outfit a number of new carrier air groups. Even if the Japanese could've increased their air capacity through more carriers, they simply wouldn't have had the planes to put on them, even in 1941 or 1942.

However, I want to delve into some of the proposals you've made, and hopefully explain why a swarm of "small" carriers would not be as combat effective or as cheap as you might think.

Again, as /u/wotan_weevil discussed, there are several limitations on carrier design that made a smaller number of large carriers potentially more effective than a large number of small carriers. This was not a new problem, as it had been wrestled with by many of the world's navy's during the treaty era, when they were deciding how to allocate their available tonnage, resulting in carriers like the Japanese Ryūjō and American Ranger. However, it should be noted that even these smaller carrier designs were closer to half or a third the displacement of their larger counterparts, rather than one-fifth to one-tenth. The arguments for these carrier designs are, as you pointed out, that with a larger number of smaller hulls, the number of aircraft available would be larger and be better dispersed across the fleet. However, interwar experimentation with these smaller designs showed a number of issues, that resulted in a switch to larger designs.

First, the smaller size meant that--especially as aircraft steadily increased in size--meant that they could operate a smaller air group. As mass was a major element in the success of an air attack (i.e. one large attack group would likely inflict more damage than a number of smaller attack groups), these limitations in size meant that a smaller carrier was likely to be less effective than a larger one. While the Japanese were early experts in coordinating aerial operations off of multiple flight decks, the limitations of much smaller air groups would've made the launching of a large coordinated strike more difficult.

Secondly, and related to the former, these smaller carriers often had difficulty operating newer and larger carrier aircraft. Even at the outbreak of the war, the Ryūjō's elevators were too small to operate the Type 99 carrier bomber (D3A "Val"), thus immediately limiting the effectiveness of its air group. While the limitations on aircraft availability for the IJN may have rendered this particular issue moot, the additional constraint on having the limit the size of aircraft in order to remain operational on smaller carriers would not have been of a great benefit to the IJN.

However, beyond the operational capability and aircraft/pilot availability issues that would have plagued a proposed swarm of lighter Japanese carriers, there were also production issues. Quite simply, by the time of the Pacific War, Japan's shipyard capacity was effectively maxed out already. IJN orders for new warships had filled both its own shipyards, while also cutting quite deeply into the capacity of the civilian yards, to the extent that necessary merchant shipping could simply not be constructed. Furthermore, the nature of Japan's geography limited the areas available suitable for the establishment of shipyards, and those area which were suitable usually already had shipyards, and also tended to be the middle of dense urban areas, making further expansion of extant shipyards difficult as well. This is not to mention that there were issues in keeping the skilled shipyard workers available to produce new ships, as well as the availability of raw resources necessary to either expand available production, or to build new ships. Thus, even if the Japanese wanted to start turning out micro-carriers, the room or capacity for such production was simply unavailable.

Hope this has helped to answer your question. Feel free to ask any follow ups.