"Apple has the right to keep illegal materials off its servers", "When my browser downloads illegal images" - but how is it known to be illegal? That's the sticky point that's easier said than done. YOU know what's illegal, but to a computer, it's just random bits of, well, bits, hence why anyone can upload anything.
This is why the CSAM database exists, but to fit your preference, it would have to exist on your phone scanning your browser, which brings us back round to square one.