I'm told that most phones have power usage spikes that exceed the power delivered by the charger, and they use the internal battery as a capacitor to soak up those spikes.

To a certain degree, that might be true. However, small batteries like they are found in phones have relatively high internal resistance (voltage drops as current draw increases). They can't deliver huge currents like capacitors. A beefy enough power supply should be able to handle power spikes even without a battery installed.