You should write a language for the same reason you should write a game.
It's not hard for a game to touch all sorts of corners of the computer world that routine work will never come near. Games are great because they're easy to focus on, you know pretty much precisely what you want it to do. They also tend to be made of small parts, yet extensible, in terms of adding features if you still have wind in your sails.
And if not, hey, you have a few more data structures under your belt. Who knows when those may come in handy again.
Languages are similar. Get past a few "hard parts" and they can be a fun ride.
For extra fun, put the language into your game. Dog food for everyone.
It's not hard for a game to touch all sorts of corners of the computer world that routine work will never come near. Games are great because they're easy to focus on, you know pretty much precisely what you want it to do. They also tend to be made of small parts, yet extensible, in terms of adding features if you still have wind in your sails.
And if not, hey, you have a few more data structures under your belt. Who knows when those may come in handy again.
Languages are similar. Get past a few "hard parts" and they can be a fun ride.
For extra fun, put the language into your game. Dog food for everyone.