I also hate this behavior. My understanding is that it doesn't get noticed by native users as it's not an issue when the JP input is the only input, so it's mainly an issue for language learners.
It's been on my mind to try the google IME for some time, to see if it fixes this issue, but haven't got around trying it yet.
The Google IME is waaaay better. With both I have some bug though where the browser will just freeze for a few seconds while switching the IME - happens in both Chrome and Firefox. Also happens on macOS with the native IME so there seems to be some bug there...
It's been on my mind to try the google IME for some time, to see if it fixes this issue, but haven't got around trying it yet.