It's not only an additional disk space, it also a need to sync it with main column, using triggers or whatever, and have much bigger backups. Why "initial instinct was to question", though? I don't see downsides still, unless yeah, weighted queries or need to search in joined tables etc.
It's a generated column, so there's no overhead to keep it up to date, but all generated columns in PG are stored. The corpus for text search will be stored 1x in the source column, 1x as a tsvector in the index, and an additional 1x in the generated column if you do so. That's a 50% increase in disk space.
