No, it is a problem exactly equal to the other one. No typewriter can produce 98,000 different characters. And no typewriter can produce 11,000 different characters.
With zero difference between hangul and hanja, how can the typewriter favor one over the other?
There were Chinese typewriters but they were very large and a lot more annoying to use. Japan also used typewriting. They just look a lot different, with a giant cylinder of tiny keys to facilitate thousands of characters. https://www.youtube.com/watch?v=wQ-SHOsbH4Y
Hangul ones were a lot smaller. I misspoke earlier; they had letter-based keyboards and mostly just did compromises on the shape of the syllabic blocks; a keyset for an initial character, a keyset for medial characters and a keyset for terminal characters. If you just assume the initial character set can be tiny to fit both the characters with and without bottom terminals, then you wind up with slightly odd-looking but perfectly serviceable typed Korean.
With zero difference between hangul and hanja, how can the typewriter favor one over the other?