I worked in automotive throughout college amd encounterd this all the time. The gash on the tire is somewhat large. If it were my tire. I would repair it. Some shops don't want to risk liability.

If you want it repaired. Try another shop. Its far enough from the edge for the patch plug to stick.

Btw the gash maybe large. But it maybe just the top last of tread. Inside of the tire the puncture may be small.

Personally if it were me and i wanted the tire replaced. I would get a pair of a less expensive brand with similar tread and speed rating.