I must admit I can't see any particular difficulty which would make the photoelectric effect more difficult to describe in terms of waves than other quantum phenomena.
It's just a photon wave interacting with electron wave that's wrapped around nucleus, exchanging portion of energy and momentum and reshaping electron wave (unwrapping it). Nowhere the is actual need for bouncing balls. Just part of this process is governed by bouncing balls equations and since we had Newton and Bohr earlier we'd rather think about it as bouncing balls behaving bit strangely than waves obeying some of bouncing balls laws.
The salient point here about the photoelectric effect is not a pre-existing mental image of bouncing balls, but being forced to explain the fact that decreasing the intensity (amount of light) of monochromatic light doesn't produce electrons with lower energy (only changing the light's color/wavelength does that). This cannot be explained with classical waves; less light waves would produce lower-energy electrons.
now we can start talking about wave-packets, but then we staring to blur the lines between what is the difference between a particle and a wave-packet.
Yup, neither particles nor waves fit the quantum world completely, but people chose to think about all this as strangely behaving particles, not strangely behaving waves which would be much easier because there would be no need for collapse of probability distribution to a particle and concept of same particle being in multiple places as waves could be naturally more blurred or more sharp.
Ultimately it doesn't matter because math is the same.
