They were originally introduced to save on processing power for the early trading computers. (Kind of like the abbreviation of 1999 to 99 that got us the Y2K bug)
Despite massive increases in processing power, big market participants have fought tooth and nail to retain the odd-lot pricing system. Because the odd-lot price discovery system both screws over smaller retail traders and is absolutely RIPE with opportunities to manipulate stock prices.
For example, get a co-conspirator or just have two shell trading accounts. One account sells a round lot of 100 shares, the other buys two odd lots of 51 & 49 shares.
The round lot sale does affect price discovery. Causing the stock to move downwards in price.
The odd lot buys do not affect the price.
Do this a couple of million times back and forth and bingo bango the stock price falls like a stone.
Do it the other way, and the price rises. The market makers and complicate Hedgefunds can 100% manipulate the price of almost any stock completely at will.
It’s super illegal to manipulate the price this way, but like that ever stopped a Hedgefund.
As long as retail holds until the liquidations start and the rules change, it’s irritating to watch, but largely immaterial.