Most words are written using a mix of kanji/hiragana/katakana, so it would be very hard to make a Scrabble-like game.
However, if you stick to just katakana, or just hiragana, you can make a fun learning tool for people!
Let's say I drew 7 tiles, and was able to make the word oishii (おいしい). The next player could then add a single tile to assemble the word sushi (すし). I think it'd be fun!