My mum (late teens when war broke out) did the same with wrapping paper, and also doing the thing with sheets. She also had a 'thing' about cutting toenails short, so they didn't wear the sheets out! Once the sheets had really had it and were irreparable, she'd cut them up into squares and use them as cloths, or for dad to use as hankies and/or polishing the chromework on the car.
I still have her button box, and her needlework basket. There's stuff in there that hasn't been touched since the 1950's. When I need some mid-grey bias binding or have some green socks to darn, the supplies are ready and waiting.
I grew up hearing make do and mend, save it for a rainy day, a stitch in time saves nine, look after the pennies and the pounds will look after themselves, waste not want not, enough is as good as a feast.
Do I save jars, tins, boxes, wrapping paper, tissue paper, ribbons, bows, bubble wrap and gift bags? You bet I do. We cut up old envelopes to use for shopping lists. And I can hear DM's voice in my head when I go round the house switching off lights to 'save the juice'.😁