The US mints about 8 billion pennies per year, which at 2.5g each and 2.5% copper, works out to about 500 metric tons of copper. Add in nickels (1.5B x 5g x 75% copper = 5600 metric tons), dimes (3B x 2.2g x 92% copper = 6100 metric tons Cu), and quarters (2.5B x 5.7g x 92% copper = 13000 metric tons copper).

Which works out to just over 25000 metric tons of copper per year used in US coinage.

About 2 million metric tons of copper are used in the US per year. So all coinage represents about 1.25% of US copper consumption, of which quarters are about half.

There are some good reasons to eliminate small coinage, but "it will noticeably help with a copper shortage" isn't really one of them.