> At least in Japanese, the sound of the character is typed out using english letters

Technically speaking, Japanese have kana-based keyboard layout, where a single mora is a single keypress rather than two. However, there is still an extra (second) keystroke for dakuten/handakuten (か -> が), which is not required with romaji input (where it's just "ka" vs "ga"), so it's not a 100% speed increase. So, typing is somewhat more efficient than with romaji, but I think I've heard no one uses that, except for, possibly, professional typists.

Just as an anecdote, I know of at least one person in my company who uses it, without being anywhere near a professional typist. I suspect older generations may be much more likely to use it.

In any case, even though mostly everyone prefers the IME on their computers, I haven’t seen any Japanese people who prefer romaji input on their smartphones.

Pinyin input for Chinese is similarly phonetic. Supposedly there is a method popular in Taiwan based on strokes.

Reading characters is a bit faster, but only because you had to memorize 10,000 of them already. People reading English will similarly chunk many of the words they are familiar with so that they are not so much read as they are recognized.

This is also a stroke system (Wubi) that's more popular and faster in China too. Maybe it's a related system to the one in Taiwan. Pinyin makes sense only if you're already familiar with the Latin alphabet and how they sound. Those are literally foreign concepts to the Chinese.

Pinyin IMEs are still much more popular than Wubi IMEs because of the latter's steep learning curve. Pinyin was designed by Chinese for Chinese learners, and is only incidentally used by westerners. It is based on the latin alphabet yes, but its how all the school kids in China learn standard pronunciation of mandarin words (indeed, this is pinyin's main purpose). So pinyin isn't really a foreign concept to any Chinese who has went to school since the 60s.

There's also a Taiwanese system called bopomofo or zhuyin, which is basically a Chinese version of kana.