the US killed the half-penny when it was worth what a dime was worth today - practically speaking, anything under a quarter is too little to be worth worrying about.
Yes, this likely means retailers will play games with change, but other times you will come out on top with the rounding. And think about it this way - yes, sometimes retailers played games with the half-penny too. A few decades on, once you've gotten out of the mindset that someone is "cheating you" out of maybe as much as a quarter-penny every transaction, nobody cares, it's not an actual significant amount of money.
there also are significant costs associated with maintaining currency units that small - it costs more than a penny to make a penny, and while sure, that penny gets used through multiple transactions, that also incurs additional costs on everybody who has to handle that penny in every single transaction. The amount of time and energy spent handling that penny probably winds up being dollars over the lifespan of the penny.
this also gives interesting context to the expression "a penny saved is a penny earned" - that expression today would be "a dollar saved is a dollar earned". A penny was actually a decently significant amount of money when that expression was coined, it wasn't literally "every single quarter-penny matters".