The hazard of which is greatly overstated. You are probably fine drinking the vast majority of alpine springs if there aren't livestock grazing nearby. I rarely bring purification and I've never gotten sick.

Purify when you can, absolutely - but if you have to choose between a stream and a spring, take the spring. Not guaranteed to be safe, but if it's popping up out of the ground, it's more likely to be safe than flowing surface water. Also, always consider what's up-stream.

This is counterintuitive to what I've learned about sediment filtration — any insight for a layperson?

Better than being dead.

“ Symptoms usually begin 1 to 3 weeks after exposure”

Water now will let you get to treatment next week.

I second this; a couple of years back I went hiking with a buddy, we had water but planned for a day hike that extended overnight, and we had to drink water from some streams. While I worried about illness, having water then meant we were able to get back to civilization, where if we got sick we could seek medical attention.