I think this is a common misunderstanding; people don't realise Paula is just a sample playback chip. They hear it produce 'chip' music and assume it's being synthesised - it's an easy mistake to make.
It was mostly used for playing back samples but it can do far more.
Paula can do:
Sample playback.
Loop playback - it's an oscillator.
If the 68K changes the waveform it's looping you get wavetable synthesis (think PPG synths).
Modulation of channels with AM and/or FM so:
- FM synthesis.
- AM synthesis.
- FM + AM synthesis.
Non-DMA playback. The processor to produces waveforms on the fly any way it pleases - You could set up the Amiga as a soft synth before soft synths were invented!
So, it is not just a sample playback chip, it's far more sophisticated.
If you want to recreate that 8 bit sound an old dedicated sampler like an Akai S2000 would do this 'out of the box'
A big part of the Amiga sound is the variable rate sample playback. It turns out a lot of gear used to do this but only very early on. You'd probably have to go back to something rather older to get an Amiga-like sound like a first generation Emulator or Fairlight.
Alternatively, just buy the right VST. There is one that nailed the Amiga sound pretty much perfectly.
Regardless of what others may say - the SID chip is unique. There weren't any pre-built synths that could sound anything like it; it was worthy of development into the SidStation.
Indeed, I bought a C64 so I could use SID.