As someone who’s pretty into spiders, I’d add a few nuances here.
Most spiders are indeed reluctant to bite humans, but I wouldn’t say they
only bite when they’re “protecting their lives.” Bites are generally defensive responses to being restrained, squeezed, trapped against skin, or otherwise threatened. Venom is metabolically costly, so there’s no evolutionary advantage in wasting it on something they can’t realistically prey on.
Also, the “they have poor eyesight” part is species-dependent. Many spiders do have relatively poor vision, especially web-building species, and rely heavily on mechanosensation and vibrations detected by their legs and sensory hairs. But jumping spiders (Salticidae), for example, have remarkably good vision for spiders and actively use visual cues to hunt.
And spiders don't necessarily mean you’ll have “no other insects.” They can reduce insect numbers locally, but they’re predators rather than some kind of natural pest-control force field.
One other thing: if a spider is crawling on you, staying calm and gently giving it a chance to move away is sensible. But I wouldn’t guarantee that it “won’t bite” — spider behavior varies enormously between species, and individual spiders can react differently when disturbed.
So yes: spiders are generally far less interested in humans than humans are in them, but their behavior is a lot more species-specific than the usual “spiders are harmless and timid” explanation suggests.