But, at a 50ha orchard site at Te Puke, Plant and Food Research scientist Dr Bryan Parkes and colleagues have been trying to do just that.
Each year, New Zealand throws $20 million toward finding the next wonder cultivar, whatever it might prove to be.
It's a huge amount of money, but every cent of it's needed to trawl through about 100,000 potential cultivars.
"We have have to evaluate every individual that's fruiting every year, and we are currently doing this for about 30,000 to 40,000 seedlings every year," said Dr Parkes, who addressed today's Kiwifruit Innovation Symposium in Mt Maunganui.
Each seedling was equivalent to around 200 pieces of fruit.
"So if you do the maths, you end up with a lot of evaluations."
Somewhere among them all, though, would surely be the cultivar that superseded the Hayward.
And the growing speed of innovation in the space was increasing the chances of finding it.
While the team have identified candidates that have superior taste and high yield, the toughest challenge has been how to genetically reproduce its exceptionally long storage time.
"I think we'll be able to reproduce it, but not until about 2030."
Meanwhile, the scientists have been able to watch the stunning success of a cultivar of gold kiwifruit selected to replace the Kiwi-bred Hort16A variety ravaged by the vine-killing disease Psa-V, discovered in Te Puke in 2010.
The more resistant Gold3 variety, one of three new cultivars delivered from Plant and Food Research's breeding programme, is now grown across around 7000ha around the world, and predicted to generate around $2 billion in sales per year by 2020.
"At the time, we honestly didn't know 100 per cent how it was going to go," Dr Parkes said.
"It looked very promising in the trials we'd done - but time has shown us it's performing exceptionally, customers are responding to it extremely well, and it's showing a very good Psa tolerance ... so we found our saviour."
Gold kiwifruit makes up about a quarter of the country's current kiwifruit exports, with Green comprising the rest, but Zespri is aiming to eventually achieve a 50-50 split between the two.
The Hayward kiwifruit: our little green superstar
• The most dominant kiwifruit cultivar in the world and renowned for its superior yield, taste and storage time.
• In the 2014/15 season, Kiwi-grown Zespri Green (Hayward) kiwifruit sold 69.3 million trays, earning around $900m in sales revenue.
• Zespri is now aiming for around 78 million trays of NZ Green sales this season.