Barebones ATmega328 - Why use caps on the crystal?

A minimal atmega328 design doesn't have the crystal either.

With a crystal and no capacitors, you are relying on the stray capacitance of the wiring and the capacitance of the mcu. This may not work reliably, and the frequency will be a little higher than the nominal frequency of the crystal.

I normally use a 3-terminal ceramic resonator, which has the capacitors built-in.