Yes that is exactly what I meant by a cheap onboard sound chip.
When you play a mod on that sound chip, 4 channels or 64 channels, it doesn't matter: The CPU has to do all the work of mixing the soundchannels together which is exactly what Amiga Oktalyzer and TFMX have been doing since the 1980s and Octamed Sound Studio and Digibooster and others have been doing since 1990s.
At least Paula can mix 4 channels together for free on its own. Your cheap onboard sound chip can't even do that.
It has 10 24-bit DACs capable of 192kHz playback that can be multiplexed down into a single stereo stream (for instance, when using headphones). In what sense is it not capable of mixing channels?
At least Paula accepts a wide variety of sample rates. Your cheap onboard soundchip can't. It just laughs at you and lazily refuses to play any sound that has not been laboriously resampled by the CPU to one of the few frequencies that it can handle.
Well, there you may have a point, but plenty of on sound chips support hardware mixing of sounds at different playback rates. It was very common for older DirectX drivers to support hardware sample replay/mixing on the soundcard before Windows Vista came along with it's entirely new floating-point based audio system (Universal Audio Architecture).
Mixing audio on the CPU, however, uses an absolutely pitiful amount of CPU time, even on any remotely accelerated Amiga (I've done 32-channel stuff in OctaMED SS on an 040), let alone a present day PC.
I can play back two dozen MP3 streams simultaneously on my current (linux) PC before I see pulseaudio lingering in the top 10 processes, and even then it's never more than a few percent of the available capacity of one core.