According to Professor Shujiro Urata of Tokyo's Waseda University, the reason is politics.
Up to 90 per cent of konnyaku potatoes are grown in the Gunma prefecture, about 100km north of Tokyo. The same prefecture produced four Prime Ministers in the past 20-30 years.
"Maybe that is why the konnyaku potato gets such protection."
Other food products also face tariffs for the same reason. For those without free trade agreements removing the tariffs, pork is nearly 400 per cent, dairy is more than 200 per cent, rice 600 per cent.
Japan started entering into free trade deals after 2002 when it became clear the World Trade Organization would not deliver the results hoped for.
Since then Japan has outpaced New Zealand in some regions - one of Japan's first agreements was with India, and it has a newly minted trade agreement with the US. It has just completed its agreement with the EU, while New Zealand's is still in negotiations.
New Zealand has long been trying to get over the line with both of those countries. But Japan is still negotiating with China and Korea, both of which New Zealand has secured.
Japan only started joining negotiations for the "mega" deals - such as the TPP - from 2013.
Professor Urata said Japan had been in a long recession and faced a declining, ageing population.
Those factors combined had impacted on both domestic and foreign investment, and Japan needed markets elsewhere to boost that.
Tomohisha Ishikawa, an economist with the Japan Research Institute think-tank, said the advantage for Japan in those "mega" deals was clear from its recent bilateral deal with the US.
Japan was forced to opt for that deal after the US pulled out of the multilateral TPP.
Ishikawa said the bilateral deal was very much the second best option.
"In such a bilateral approach, the strong country is strong. The weak country is weak. The US can leverage the power of the US.
"But in a multilateral approach, small countries are not losers in negotiations."
The bilateral deal excludes Japan's most lucrative export: motor vehicles and parts.
"The US had agreed [to drop the tariff] in the TPP," says Urata. "But then along came Mr Trump."
It would be akin to New Zealand signing a deal that excluded cows.
Urata points to the reason Japan went ahead with the deal anyway: the US had threatened to boost tariffs on motor vehicles up from 2.5 per cent to anywhere as high as 25 per cent.
Japanese officials also make no secret of the Government's impatience at the line the US has taken under President Donald Trump.
But they are also very keen for the US to eventually join the Trans Pacific Partnership.
In the meantime, the reasons for Trump's stand are the same as the reason for the tariffs Japan keeps on many of its agricultural and horticultural products: politics.
Every country has its konnyaku potato.
That humble, high-tariff potato has many other nicknames. Among them is Devil's Tongue.
* Claire Trevett is in Japan as part of a journalists' programme funded and organised by Japan's Ministry of Foreign Affairs.