A household wrapping for four to six people gets through roughly three rolls of wrapping paper each Christmas. Over five years that is fifteen rolls bought, used once each, and thrown out.
Why most of it cannot be recycled
Foil finishes, glitter and plastic lamination are all common on Christmas wrap and all three contaminate paper recycling. The quick test is the scrunch test: paper that springs back open rather than holding a scrunched shape has a plastic or foil layer and belongs in general waste. Sticky tape left attached does the same thing.
What replaces it
A reusable fabric bag set is bought once and still working five Christmases later. Three bags in small, medium and large cover most of what goes under a tree, and a bottle bag handles the one shape paper has never wrapped well.
The objection worth taking seriously
Children like tearing paper. That is real. A drawcord bag pulls open with the same rush and no mess, and households that switch usually find novelty carries the first year and habit carries the rest.