Report Generator for Schedules
Revit needs a separate report generating program/module to allow schedules to be formatted correctly for printing. Exporting to Excel to do this shouldn't be necessary.
Many schedule types are not generated to be placed on drawing sheets and often run to multiple printed pages.
A report would take the columns and data from an existing schedule - which would govern the filtering, sorting, columns used/hidden, grouping, column order, column header names etc. of the data on the sheet, but the report would have it's own page size, page orientation, headers, footers and when printed, would break the schedule rows across pages based on the space available between the header & footer.
It would be up to the user to decide how the columns can fit across the page width by managing the columns in the schedule and the individual column widths, page width and page orientation for the report.