The ¥1000 coin is only for commemorative purposes unfortunately and isn't generally circulated. Though we do really need one in general circulation, because with inflation, that ¥500 coin is rapidly becoming much less useful than it once was.
Yeah I agree with you for why it stick around. I think also the mint was stuck on the idea of not rocking the boat. No new bold designs, no bringing back lady liberty and beautiful designs, no experimenting with coins for other values than what we've always used, just maintain the status quo. Even though they could easily bring back a $2.50, $5, and $10 coin and that would still be tradition since we had coins at those values at one point.
I agree with you, a great first step would be finally stop printing the dollar banknote and release all the coins in storage. Get rid of the $5 and $10 next, but at the very least do that first step.
But no one at the mint wants to rock the boat.