It's worth bearing in mind that the source is Japanese. All input methods for the Japanese language are a compromise. Inputting kanji on a physical keyboard is nowhere near as fluid as inputting Latin characters - you're constantly toggling between inputting kana and selecting the kanji options presented by the IME. The prediction and correction technologies of smartphone keyboards are a very good match for kanji and…
As a native Chinese speaker I find the opposite.
>when the hànzì are presented directly above the on-screen keyboard
It's basically the same for most of "proper" PC IME. They start to appear when you're typing pinyin, and then you choose with numbers or space (for first one).
Showcase: https://i.imgur.com/gQGKw11.gif
So, IMHO there is no obvious advantage that smartphone's IME has over PC's here. And the speed of typing on physical keyboards beats smartphone by a mile, overally speaking.
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However, I DO found that most of Japanese (which I'm a second-language user) IME on PC I tried having the problem that, you have to press some key (normally `enter` or `space`) to start "convert", and even another input to start choose between candidates, which is very tedious because you have to keep pressing `space` which IMO shouldn't be necessary
(Note: It was how most Chinese IME (Like Zhineng ABC) worked 10 years ago, but they got rid of redundant inputs later.)
Showcase (MS JP input, I knew it's not the best, so feel free to let me know how other IME function in these scenarios!): https://i.imgur.com/hwml1Sf.gif
Notice that I have to press space once first to enter "convert mode" (which breaks down your inputs to groups), and then press space again (for the first group) to make the candidates appear. I really don't get why it can't be like the Chinese IME.