For this processor to continue dissipating 335W without overheating, it needs to dissipate that 335W of heat energy into hundreds of cubic feet of air every minute. Six fans push and pull the air through hundreds of tiny fins, which are conducting heat out of liquid coolant continuously pumped through tubes soldered to those fins and through a giant copper waterblock millimeters from the point where this heat is produced. And even with all that, it probably can't actually run at 335W continuously.
You don't have a $200 cooling solution on every foot of your battery cables, they're wrapped in PVC or silicone, buried in conduit, in plastic wire wrapping, or through insulation in a wall cavity.
As an EE, those rules are painfully applied to microprocessors, such that a ton of PCB design energy, mechanical constraints on packaging, and other costs are spent removing that heat. You have the convenience of just buying the recommended AWG4 cables and it just works, regardless of the severely sub-optimal thermal design you might employ when running that cable.
In theory your batteries could pass 255A through a single strand of bare copper from an Ethernet cable for a few tens of milliseconds before it went into thermal runaway and liquefied/evaporated. Remove that heat fast enough (liquid nitrogen?) and you could run tiny cables to your battery storage.
Sadly waiting on cache (l1, l2, and l3), main memory (4 32 bit channels approximately 100ns away), missed branch predictions, etc is fairly common. So delivered performance is much less than you'd think form a 6 way issue @ 6 GHz * 8 to 16 cores. Sadly we are still stuck at 128 bit wide memory, as a result even the most parallel of codes like cinebench go up by 50% when you double the number of cores.
Also consider that there's 10+ billion transistors for those 200 A to go around.
As far as power density goes, the i9-13900K seems to be 335W / (257 mm^2 die area * ~1mm water thickness) ≈ 1.3e9 W/m^3. The power density of the sun in comparison is around 2.8e2 W/m^3, roughly what you'd find at the center of a large pile of compost (although the temperature at the sun's core may be just a wee bit higher).
The sun's output is 3.8 x 10^26 watts and the volume is 1.4 x 10^27 cubic meters
Surface of the sun is 6.09×10^12 km^2, which comes out to 62.4 watts per square mm. The AM5 socket is 40x40mm, so that would be 100,000 watts of the sun's surface.
Dynamic power being proportional to voltagr squared will hurt perf/watt significantly also.