This is much worse than not learning cursive. Spelling is important, you cannot always rely on spell check. I work at a computer all day long but I still need to know how to spell! I am one of the few employees on our campus that are always called on to proof read important letters, emails, etc. You would be shocked at the folks that cannot spell anymore. The English language is too complex to depend on spell check. As long as its a word, spell check won't catch that its the wrong word. Using a dictionary is a great skill (one I have to work on dd with because they don't use them in her school), but you still have to have an idea of what you are looking for to find your word.
DD (12) is taking a computer class that is teaching word processing, spreadsheets, powerpoint, and data base. They will find all the useful sites on the internet for doing research and have the basics on using the computer. But, even with this class their Language teacher finds it necessary to give them spelling words/tests, hand write some of their shorter essays without the use of the computer except for research. She also lets them use the computer for some things, let spell/grammer check tell them something is wrong and then has them correct it on their own.
The English comp instructor at the community college I work for was thrilled when I told him all of this. He said he is shocked every year at the few skills the students come to his class with. He says that too many students depend on spell/grammar check so much that they don't realize how many mistakes they have made. He says he is really saddened seeing so many students get to a college level and cannot spell or write a correct sentence without a computer saying how to spell the word or telling them they have written a sentence fragment.