It's not just chips. Japan's generally protectionist/sheltering attitude towards businesses makes their whole economy structurally inefficient. Japan's nominal GDP per capita is like 40% lower than the US these days.

There is more to life than GDP per capita.

Yes, but economic productivity is still pretty important.

Surely there is a middle ground between "stupid chip shortage" and "loss of local agriculture" though. Japan can grow potatoes and trade them too.

Like I said, everyone does this to some extent. But Japan is among the worst

That middle ground would be something like price regulation. Instead of just imposing quotas or forbidding imports of specific goods, require the imported goods to be sold at the market rate of the locally produced good.

It would allow imports to prevent shortages in the market without killing the local producers because there is no reason to stop buying from local producers if the imported goods cannot be sold at a price lower than what the local producers are willing to bear. Distributors would continue buying local, while also adding some imports as a cushion against production fluctuations.

Tax the difference between the local market price and the lower imported good price, when the imports are cheaper. Don't tax when the import is at the same cost/more expensive.

Why is local agriculture more important than local customers?

The idea from what I gather is that the country is capable of supporting itself, and did for centuries, and shouldn't let industries wither and die for short term profit that would kill off industries that allow that ability of self support.

Because being self-sufficient and having a good import/exports sheets makes you more resilient in the mid- and long-run that having all the chips that local customers demand.

You can always allow for more chips whenever you really want. Reversing a damaged trade deficit or self-sustainability? Not so much, and not anywhere near as fast.