The piece system originates ...
There is a lot of history here.
In the late 60s the US CAB (precursor regulator to the DOT) spend a couple of years investigating what baggage allowance airlines should give in those ultra-regulated days. After extensive studies, hearings, and pencil pushing they came to the conclusion that 'cube', or volume, was more important than the weight. The decried that US domestic airlines all had to give 2 pieces free with a maximum weight of 70lbs each. Since they also regulated international baggage rules by acting on IATA agreements they disapproved IATA's 20kg maximum weight for Y (and 30kg for F, no C/J then) and 'ordered' that their piece system had to apply on all journeys from or to the US. While the Canadian government didn't do the same, the Canadian airlines insisted the same rule had to apply otherwise they would spill traffic across the border. Other airlines didn't want to apply the US rule everywhere so we ended up with two systems.
The DOT continued to regulate IATA baggage agreements until just a couple of years ago (although airlines had begun to abandon multilateral agreements at least 10-15 years earlier). As long as they had the power over IATA agreements they refused to permit any changes from that 60's era decision - however the free pricing clauses of open skies agreements meant they couldn't regulate what individual airlines did. More and more airlines began to 'do their own thing' and we have what we have today - a hodge-podge of different rules, prices etc.
IATA still has 'rules' for baggage but they no longer fix the pieces, weights and/or prices. They are only technical rules that provide the means for one airline to sell another's services on it's tickets (combine two or more different baggage rules on one ticket).