People want their documents (or queries) free of spelling errors. That is their pain and that is the challenge.
The example sentence has misspelled words, hence is within the domain of spell checking. This type of misspelled words are called "homonyms", which are one very common spelling problem. The academic terminology is uninteresting to most users, however.
Or if you mean to posit that "spell checking really means looking up if a word exists in a static dictionary of English", then yes, that's easy and solved, no argument there.
The example sentence has misspelled words, hence is within the domain of spell checking. This type of misspelled words are called "homonyms", which are one very common spelling problem. The academic terminology is uninteresting to most users, however.
Or if you mean to posit that "spell checking really means looking up if a word exists in a static dictionary of English", then yes, that's easy and solved, no argument there.