We should not violate the global data to track the output data
while it is constructed and printed.

Most of the time, we actually clear the output data anyway --
either before constructing it, or after printing it.
In some cases we didn't, but I think that is a bug. It's really
hard to keep track of this.

The output data should belong to a certain scope and get destroyed
afterwards. Passing it around is very confusing. Don't do that.