That then introduces ease of use problems. You won’t be able to log in to another device without copying your key over from an already logged in device for example.
Web browsers don’t usually allow access to local files made outside the browser, so even logging in between browsers would require having your key on hand.
Not to mention if you lose the file containing your key (hard drive craps out, etc), you’ll lose access to your account entirely. So users would be forced to backup their keys.
Not issues that would make the product unusable, but enough of a hindrence that 90% of users would just go find something else (like threads) to use instead.