"your twenty bucks will be worth forty bucks just by getting rid of the penny."
That'a ridiculous, twenty bucks would be worth twenty bucks still,
except that by getting rid of the penny prices would have to be rounded to the nearest .10 or .05 which would of course be upwards which means inflation. Even if slight, ie $1.99 to $2, it still is up.
Plus that .99 gives consumers the illusion of less, making the price of whatever item more attractive and thus tempting to spend. That's why things are priced that way. Sure, you can price it $1.95, but that .04 lost adds up to a hefty chunk of cash by year's end for business and they're not in it to lose 4% of potential earnings.
Then there's taxes. NYC sales tax is 8.875%. Ok, rounding it up to 10 doesn't seem like much, but again, it adds up, then there's again there's the optics. It used to be 8%. Then it was 8.25. If they raise it again from 10% - and one day they will - it would have to be to 15%. That'd be nearly double what it was in the 1980s and people won't be liking that and officials won't get themselves reelected.
And once again in terms of optics, getting rid of the penny would be seen as a concession that our money is weaker. Eventually the nickel will walking the plank, and folks won't like that either. Consumer confidence = consumer spending. Just ask the aftermath of the Great Recession of 2008.
The penny may cost more to make then it's worth, but part of that calculation is transportion. A cheaper metal composition can help offset that, and it something the US Mint is experimenting with.
A dollar coin is more cost effective in the long term, but we're not switching because people are reluctanct and also because of lobbyists from the dollar bill 'paper' making company in Massachusetts. You'll have copper, nickel, and zinc interests hollering for the penny and politicians listen to them. That's why dollar coins tarnish so quickly and ugly, because of zinc and tin lobbyists getting some squeezed in...
Then finally there's tradition. We like the penny. We like a lot of seemingly outdated things. We were supposed to go metric decades ago (signed into law by Carter in 1976) but we simply didn't go along with it. Pennies may be practically worthless but people like them. That's why it's still around and not aluminum like was planned in 1973.