Appreciate the civil discussion, so let me just say that I suspect you never typed in the numbers and tried to quantify the danger of nuclear waste. Let's try a quick and rough estimate.
The energy density of uranium is roughly 80,620,000 MJ/kg [1]. Existing nuclear power plants have thermal efficiency between 30-40%, roughly speaking [2], so let's be pessimistic and choose 30%. That means actual usable energy density of uranium is 24,186,000 MJ/kg, or 6,718,333 kWh/kg.
The world produced 27,644,800 GWh = 27,644,800,000,000 kWh of electricy on 2019 [3]. If we used nuclear to generate all of this, we'd need 4,114,830 kg of uranium, or 4,115 ton per year. Let's round up to 5,000 ton.
Spent nuclear fuel contains about 0.8% plutonium 239 [4], so our 5,000 ton of uranium will generate about 40 ton of plutonium 239, with half-life 24,000 years and radioactivity of 2.3 GBq/g [5]. So our hypothetical nuclear waste will have radioactivity of 2.3 GBq/g * 40 t = 92 PBq. Which is a lot.
...or is it?
Potassium, naturally occurring and essential for life, is naturally radioactive (31 Bq/g), because it contains 0.012% K40 [6]. Seawater is about 0.04% potassium [7], which contributes to a natural radioactivity of 12.4 Bq/kg, or 12.4 kBq/t from potassium alone.
Actually, let's forget the earth. Let's spread the nuclear waste evenly on the Mediterranean - volume 3,750,000 km^3 [8] - who needs Italy anyway?
It contains 3,750,000,000,000,000 ton of seawater, or 46,500,000,000,000,000 kBq of natural radioactivity, which is 46,500 PBq. So our hypothetical dump of plutonium 239 will increase the Mediterranean sea's natural radiation level by about 92/46500 = 0.2% per year [9].
A far cry from extinction of all known life, I have to say.
* By the way, you may want to re-consider before saying stuff like "Pu239 has half-life of 24,000 years - it's not safe!" Coal, for example, contains tons of mercury, which is not radiactive (i.e., it has a half-life of infinity). After 24,000 years, there will be 50% of Pu239, but 100% of mercury left from coal ashes. Which is worse?
[1] https://en.wikipedia.org/wiki/Energy_density
[2] https://www.world-nuclear.org/information-library/current-an...
[3] https://en.wikipedia.org/wiki/List_of_countries_by_electrici...
[4] https://en.wikipedia.org/wiki/Plutonium-239#In_nuclear_power...
[5] https://www.radioactivity.eu.com/site/pages/Plutonium_Proper...
[6] https://en.wikipedia.org/wiki/Potassium
[7] https://en.wikipedia.org/wiki/Seawater
[8] https://en.wikipedia.org/wiki/Mediterranean_Sea
[9] Of course the actual effect will be higher because there will be other isotopes, shorter-lived and more radioactive. That's why I proposed keeping the waste in a fridge for 200 years first. I'm not a monster.