Remove electrolytic capacitors for a class-D amplifier
The application diagrams in the datasheet use 470 uF capacitors as local supply decoupling. 

My guess is that removing (or lowering the value of) these capacitors will decrease the peak power that the IC can deliver to the speakers.

These capacitors are local energy buffers that can quickly supply high currents to the amplifier when it needs it. The supply is relatively "far away" meaning more series resistance and it might not respond quickly enough to supply enough currents to prevent the supply voltage from shortly "dipping" under peak load conditions.

The fact that TI uses huge capacitors on their evaluation board means that they do serve a purpose. Huge caps mean increased cost (the capacitors themselves) but also increased PCB space usage. TI would only do that so that they can "show off" what the IC can do.

So if you want to get the most (peak power) out of the IC then do as they do on the evaluation board. If you want a different compromise then sure you can safely decrease those capacitors to 470 uF (because that's what the datasheet shows).

You could try to use capacitors that are even smaller than 470 uF but then performance might be impacted, you might not get the same figures as listed in the datasheet.