I agree to some extent.The problem is that after the 8th grade, most teachers do not teach spelling, or any other facet of grammar and rules of the English language.
However, if by teaching spelling you mean giving a student a list of words to memorize, then no, I don't agree. Most educational experts will agree that rote memorization is not effective with students.
The best solution would be teaching spelling, grammar, etc. through actual experience. For a student, this would mean actually writing. By having to write, they are forced to spell correctly. Additionally, students can be taught spelling through their literature they read in the classroom.
As for spelling problems on the web, that's a whole other ballgame. Hopefully this answers your question.