It won't be embarrassing if no one else in the room can spell better than you. (I once had a Chinese professor forget how to write a certain character while writing on the blackboard. He just laughed it off.)
It's also not clear to me that spellcheck will lead to people forgetting how to spell, since it's all about notifying you of spelling mistakes.
So we should study things so we don't get embarrassed? Moving on are you embarrassed because you don't know how to swordfight or any other outdated skills?
That's begging the question. It's not an outdated skill if there are situations you need it! If I couldn't spell the things I were writing on the board in tutorials, it would quite reasonably look like I have no idea what I'm doing. Not a great look.
I think in the entirety of my 16 years as a student, I probably wrote less than 100 words total on blackboards or whiteboards. There weren't computers or ipads in those classrooms either.
Whiteboards are something I use more often at work these days, but not really when I was in school.
It's utterly bizarre to me that people in this thread are seriously suggesting that spelling is an obsolete skill.