There are some around (I remember seeing something on rare input methods). But most people, native speakers included, use romaji input method. Second most popular is direct kana input. Radical/handwriting methods for unfamiliar kanji you need to look up only.
Imo you'd be better off learning to type the way most native speakers do, which is a useful skill by itself. If you feel the need for writing practice other than pen and paper, there are smartphone apps and ds games and so on.
Using the phonetic IMEs aren't that difficult and it's something I can already do with ease. I won't forget it anytime soon! I already practice with a pen and paper currently but it would be nice to have the extra practice when using the computer. If all the times where I typing Japanese was also helping me to practice writing Japanese it would seriously cut down the amount of time that I have to go over forgotten characters (which happens a lot because I type a lot).
Do you happen to remember the name of these "rare" input methods?
I think one was "tut code", but I can't remember if it's done by inputting radicals or by some other technique. There was something else which used a specialised keyboard. I think for doing live captioning or something else that needed speed.
I'm still not convinced that any method of keyboard input will help you remember the handwriting side that much. If you have a smartphone, ds lite, or other touchscreen device, there are games/training software you can have a go with. I like the ds ones since you use the stylus so it "feels" more like writing to me.