I find it easier to do kanji writing questions on mobile compared to when I'm using my laptop's trackpad. Given that there are already quizzing options for "don't use on mobile" for certain question types, I think it would be nice if we could set writing questions to only show up on mobile.
I guess that would be useful, but I doubt it will be a priority for Michael. In the meantime, you can achieve something similar by creating separate schedules for writing vectors which you use on your mobile device only.
This would be nice, but I would recommend the separate schedules.
The reason it works for those other question types is that there are still other question types that can be used for those study vectors (onyomi and kunyomi).
For writing and listening, to "not use them on mobile" is to say "turn these vectors off and redo the summary data depending on what device accesses it", which is unfortunately much more complex.