One bit reason with Japan's former colonies is that an intentional shift away from Japanese was a major part of post-colonial changes, with the express goal of undoing (or re-doing with something else in the case of Taiwan) what Japan had instituted as language policy. The KMT in Taiwan forced Mandarin on everyone to disasterous effects, and Korean saw a huge push in public spheres including a major shift toward hangeul that had previously existed but been pretty marginal in its use.

At the time, Japanese colonies functioned with Japanese as the official language. The reason that stopped in places like Korea is because use of Korean became a significant nationalist tool, and in places like Taiwan, it's because people like Chen Yi under the KMT government undertook extreme efforts to stamp out Japanese in favour of Mandarin (which itself was/is something of a coloniser's language).

In both Korea and Taiwan, Japanese became the language people had to use, but this was done gradually. The Japanese government pushed this through in three phases over many years, and at least early on in Taiwan people were encouraged to continue learning Hoklo and Hakka, the two local Sinitic languages. These were only banned much later in the occupation, in the late 1930s. I'm not defending their actions in saying that. I only mean to illustrate that the ban on Chinese was gradual, unlike the KMT's immediate ban on Japanese under Chen Yi starting in 1945. From 1945-1947 the KMT government forced many large-scale changes on Taiwanese society, and in 1947 with the massacre of protestors it became a police state, with linguistic policies only relaxing around the mid 1990s. Borring from a previous answers I've given here:

In 1945 the Japan gave Taiwan to the KMT from the Japanese. From then to 1947 the KMT instituted all their plans to rid the country/island of Japanese and make Mandarin both the de jure and de facto language. It went okay. 1947 saw the 228 incident (so named for being on February 28) which resulted in a lot of Taiwanese people dying at the hands of soldiers send by the KMT government. Was this really just about language? No. Was language policy a huge part of it? Yup. Inline tldr: Japan Japanified Taiwan linguistically in three stages and it went really well, relatively speaking. By 1945 aboriginal people had good jobs using Japanese and despite all the other terrible stuff that happened under Japanese occupation, by the end of WWII things were stable and relatively okay. Then the KMT was like no! and made Japanese not okay in public life more or less overnight, meaning all the high class people who were cool using Japanese and the aboriginal people who needed Japanese to do their jobs were suddenly not able to do that. People were angry. People protested. The White Terror began. Chen Yi was the guy in charge of this. He didn't last long. His efforts to enact KMT policies resulted in a loss of position for Japanese0speaking members of indigenous groups and ethnic Han elites. Followed by rising anti-government sentiments ultimately peaking in 1947 with the 228 Incident.

It wasnt until 1987 that punishments for using languages other than Mandarin were revoked. It wasn't until 1993 that these "minority" languages could be taught. It wasn't until a few years later that you got the founding of the Council of Indigenous Peoples and Council for Hakka Affairs. And it wasn't until 2016 that the government really apologised for how crap they were about the whole thing, with Tsai Ying Wen's inaugural address upon becoming Taiwan's president.

So What you had was, under Japanese rule, a brutal but gradual prohibition of speaking non-Japanese languages, which lasted until the KMT took over in 1945. I say gradual because they actually did it in a pretty effective way compared to the KMT who, under Chen Yi, botched it bad. There were basically three phases under Japanese rule (in Korea as well), each more restrictive than the previous one. Initially children could still use Hokkien and Hakka, and even learn them in school, but by the end of the Japanese occupation really only Japanese was okay for public life. This actually resulted in a situation where by the early-1940s you had Japanese as the language of everyday use in professional settings, and with the sort of social support that people in the indigenous population were using it and having pretty good positions in commercial endeavors because they were able to rely on Japanese. The gradualness of Japanese language policy was such that by that point, enough people had grown up with it that they were comfortable to use it. I knew of some elderly Atayal folks who still to this day use Japanese with each other, since it's what they grew up with.

The problem thus came around 1945 when the KMT took over and with heavy hands shut down all Japanese use, essentially demanding everyone use Mandarin, a language not native to the island. Today, President Tsai talks about Taiwan's indigenous languages, by which she means Aboriginal languages but also Hakka and Hokkien. This is a massive change of pace for Taiwan, which basically effectively outlawed all public use of non-Mandarin languages until the 1990s. The Mandarin policy kicked in right away, people protested, and it contributed to the crackdown that hit its peak with the 228 incident. But for the most part, no one but the waishengren were using Mandarin at home, and they were almost entirely limited to places like Taipei. Places like Hualien and Hsinchu had large Hakka populations, as well as a few Hakka pockets elsewhere further south, but otherwise once you got to Taoyuan it was Taiwanese (Hokkien) until you hit the southernmost point of the island (Formosan languages aside, but those which were spoken in the lowlands were effectively wiped out entirely by the Japanese).

So anyway this whole period under the KMT was incredibly effective in wiping out Japanese as a lingua franca and at least in the north shifing things pretty immediately and completely toward Mandarin for most things.

In Korea, things were a little different. The short version of that is that Japan had a different and slightly weirder approach to policies there, in which they saw Koreans effectively as ethnically Japanese, or at least Japonic, as a more primitive versions of themselves. The Taiwanese were Other and the Chinese were Other, but the Koreans were seen as being both an oddity to be conquered but also a window onto themselves. This is discussed really well in a book called Primitive Selves which I highly recommend. The other part of it was that Korea had long looked to China as not just the source of superior culture but rather the Culture™, and Japan had a lot of work to do to try to break those ties. One way they did that was some early support of Korean literacy and promotion of Hangeul to try to get Korea to stop using Chinese characters, but this was more readily used to oppose the Japanese. Japan just had different goals and different things to get past in order to achieve those goals.

If you're curious about this topic as it relates to Japan's colonies, I'm happy to go into more depth here. I also did an episode of the AskHistorians podcast a few years back where I discuss the subject with 400-rabbits (the host) for about an hour.

tl;dr: Because getting away from Japan's highly effective yet oppressive language policies was a major goal of post-colonial governments.