Computers have changed all that. A computer with a good word-processing program makes it possible to compose and revise as you type. The delete key zaps any text that you would have crossed out on your longhand draft. You don't have to make your word-processed draft perfect because you can always change it. You will likely find, in fact, that the ease with which you can move text around and make changes will free up the writing process for you and make you a better writer.
Old habits die hard.
I you've always composed in longhand before typing, you may find it difficult to break out of the routine. For some students, the two-step process will always be the most comfortable way to write. Indeed, some of the world's most successful writers still do their initial drafts in longhand. If you can learn to cut the two-step process down to one, however, you can save yourself enormous amounts of time. The faster you can write a paper, the less you have to fear and dread about the writing process.