This is a logged operation, and so two copies of the index are needed until the reindexing is finished.

Your databases are growing because you have not properly sized them. The database should have enough free space for normal operation, including reindexing, as well as enough space for data growth for the next month at least. Maybe people ensure they have enough space for 3-6 months.

You want to manage your space, not expect autogrow to do it for you. Make the files large enough for operations, and grow them periodically, a few times a year.