$1 per card where many cards will be thrown away isn't money well spent. It's like handing out $1 bills.
Its a form of marketing and every penny is worth it for that 1 potential client. All you need is one session booked and youve made the money back. I always get compliments when handing out cards and have seen return business well a year after the fact. Last thing I would do is cheap out on cards. In the grand scheme of things, its a minimal cost.
You should also be selective who you hand out cards to. I don't go around the street tossing them in the air. You have to gauge who would be a potential client and I always give some cards after a session for that person to hand to their friends. Something even as simple as "hey check out these cool cards the photographer I shot with gave me." Its practically free advertising. People pay $1 a click on Google ads, but suddenly its too much for business cards? Each click is a potential client and if they don't buy, its a dollar wasted, but the traffic generated is worth it in terms of potential. Same deal with business cards.