The inductors are an array of 0.33uH coming off the DC-DC switching voltage regulators, 1 for each. They're in parallel with each other, 0.001 Ohm resistors, and the tokins. The tokens do have some internal resistance, but I don't think it's significant. Anyway, the purpose of the RLC is to tune the filter to the frequency and bandwidth of the switching noise generated by the voltage regulators. If left unchecked it would reap consequences for the processors and memory, as the ripple and noise would steadily kill them (along with artifacting, random freezing, & related shenanigans).
Anyway, an elaborate second stage RLC filter like this very efficiently removes switching noise - does so without much resistance. So the processors are free to chug current as fast as they like without burning the filter up. That said it does have a 105C temp limit for the components rated lifespan, but the cooling solution should keep that in check, if the TIC is good and console isn't full of dust - both of which we know happen in the real world. So they can and do fail, specifically the NEC/TOKINs. But does this failure occur before a BGA defect? That depend on how well designed the board and cooling solution are, the manufacturing process of the processors, thermal cycles, delta T, and much more. So who knows?!
Back on topic. Second stage RLC filters are an iterative process (trial and error), because parasitic inductance, capacitance, and resistance in the board and components cannot be predicted accurately (real world vs. theory). This is why 4800uF capacitance is actually an important factor not to significantly increase/decrease. The general advice of adding capacitance being fine, is false in this case. It would shift the resonant frequency the filter and make it less effective - detune it. Only a proadlizer has as good of a frequency response curve as the tokins had. So the best replacement for a token is a new proadlizer. Tantalum caps are the next best option and they should work fine, so long as you match the capacitance and ESR of the array they're replacing.
I spent all summer studying this circuit, so I feel confident this is correct. However, I have not been able to prove it, since all my consoles have had BGA defects and I haven't had a successful reball yet. I keep botching it. I did measure the noise with an oscilloscope and my tantalum array outperforms the worn tokins on the board I compared them to (in theory), but I can't speak to reliability or stress testing because I need a working console and I'm not about to rip the tokins off a working console...lol!
