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You're missing the insane energy density of a nuclear reaction. The first nuke used in war weighed 4700kg and produced about 88 terajoules of energy. That's about 19 giga joule per kilo
1 kg of rocketfuel + oxidizer produces 13 megajoule.
So even at 1% energy conversion for a nuke and 100% conversion for rocketfuel, the nuke is still 15 times more energydense.
And if you don't use nukes from the 40s, a modern thermonuclear bomb packs 2000TJ into 200 kilos, for a convenient 10TJ per kilo, or 7700 times more power per kilo than liquid rocket fuel.
Also the actual propulsive force would have been more like 50%, not 90. So more like almost 400,000x more power per kilo than liquid rocket fuel.