Web might not be ready... but...
... it's far less frustrating to use than the application.
Yeah. When I first started doing this course on web back in April, most of my answers were rejected if I used kanji in that circumstance.
However, each time a sentence is rejected and I know that the kanji definitely should have been correct, then I simply report it. They've gradually been adding many kanji alternatives as accepted answers. This issue has certainly improved a lot these last five months.
Now, much of the time I can go completely all out with kanji and it accepts the answer I type. Here's an example from the 6th skill in the tree, "Introduction 2":
Source text: Of course I'm fine.
Suggested answer: もちろんげんきです。
My answer: 勿論元気だ。
The suggested answer is also how the answer is displayed in the app. But on web it even accepts me typing that answer above, where I used a rare kanji like 勿 and used だ instead of です. ^^