Bill Tindall, E.Tn.
If people tried the proper abrasive composition and particle sizes this technique would be more popular. Easily crushed silicon carbide used in larger particle sizes leads to short abrasive life. Abrasive companies recommend skipping at most one mesh size when abrading wood or metal. By stepping down particle size in small increments only a few strokes of metal on abrasive is required before moving on to the next size. The benefit is rapid edge preparation and long abrasive life. A 3 x 12" strip of abrasive will last dozens of sharpenings. I have a strip of 80 grit zirconia paper I have used (occasionally) for years.

The only disadvantage of using abrasive sheets is the necessity of using a jig to maintain the tool angle across the series of abrasive sizes.

As an alternative to PSA paper one can use spritz of 3M "repositional contact adhesive" on the back of uncoated paper.