It's not just the spike, but the battery is supplying more power than the adapter for sometime extended periods of time. It would take an expensive, or very large, capacitor bank to hold enough power to accomplish that for very power intensive apps. Capacitors are good at charging and discharging quickly and lasting many more cycles than a battery, but no where near the capacity.

What you really need to know is exactly how much power the battery can provide and adjust the power supply to be able to supply that on demand and just enough capacitor capacity to smooth out the initial spike until the power supply gets the power up. I haven't done the research to know the exact amounts, but I have a lot of experience with electrical and electronics in general, both professionally and amateur. So I could probably build it if o knew the exact specs.

That or adjust the phone firmware to limit the processor and GPU speeds, but that's only possible on some phones that have code available and a way to root it without some hardware switch killing the phone permanently.