Except that is hardly unique to nuclear waste. A wide variety of industrial processes produce high grade chemical waste, especially electronics like computers, solar panels, and inverters. This is just as deadly as any nuclear waste, and if stumbled upon will kill just as quickly in a hundred years, a thousand years, million years, or a billion years.
There is however a well established solution to this problem, and that is making sure the government knows what and where it is as well as that someone it monitoring and securing the site. The actual chemical makeup of the stuff that kills you doesn’t actually matter all that much compared to makeing sure it stays where it’s supposed to be.