Different people are good at different things. In the real world you can probaly choose which way to write it down.
It also works the other way round. Students who are not as good as losing computers also write by hand. People are good at different things and work differently which does not make them less intelligent.
In a lot of colleges, assignments (not exams) usually have to be done on a computer/word processor so they can read by anyone. Not everyone can read certain handwriting after all.
Also, students with dyspraxia may have impaired handwriting, which will make it harder to read and because a lot of examiners can't be bothered to try and translate what's been written or make an effort, they'll mark the student down, even if the content is good. That isn't very fair.
But I think as long as it can't connect to the internet, games, etc, that it would be fair for students to use word processors.
School is about preparing kids for the real world. In today's world computers will be their main source of writing, handwriting is used for quick things but not for serious things.
It means teachers will have less trouble understanding children's writing. It will also mean kids with dysgraphia won't be in pain when they write and go slower because of their handwriting difficulties.
I use a word processor for my public exams and it has made my academic life almost infinitely easier. It allows all students to be judged on the same level by taking the legibility of one's writing completely out of the equation. Students shouldn't be punished for an inability to sustain neat handwriting, hand cramps, dyslexia, et cetera, hence all students should be allowed to type their exams.
If exams are supposed to be about testing the academic ability of a students under the same restrictions, then one student should not be allowed to type their essay (which is easier and lets them write faster), while another student will be made to handwrite an essay just because they have the ability to do so.
One of the most important things students can learn at school is how to interact with others. In the working world, we sometimes have the option of writing E-mails or typed messages, but often we must rely on handwritten messages. I think learning how to improve one's penmanship and ability to hand-write documents of all lengths is important. Of course, using a word processor may be the right option for a specific course or exam, or for an individual with a particular disability, but it should not be the rule.
Writing (or rather cursive writing according to the study) apparently aids in brain development specially in the areas of thinking, language and working memory.
Cursive handwriting especially has been shown to stimulates brain synapses and synchronization between the right and left hemispheres.
And I believe, personally, creativity flows better through the pen.