1. When might 'exposure bucks' be a good thing?
In my experience. Never.
2. On what conditions might you accept such an offer?
Absolutely fking Never again.
3. Does the person offering need to have a certain amount of popularity/following to make it worthwhile?
The significant amount of popularity I would require also means that this person has the money and SHOULD have the human decency to pay me for my work.
4. What alternatives to offering 'exposure' can you think of (that isn't purely monetary)?
That benefit the person doing all the work? None really. Unless we're talking trades of goods and services, and even then it would most likely have to be something I need... like I would need money
I used to do a lot of 'for exposure' work with organizations that HAD the numbers and followers, most notably being anime conventions that had thousands to ten thousands of attendees attending. It got me absolutely nothing. No additional business, no new offers, no instances of my art getting more know. Absolutely nothing except all the time and money I lost drawing art for their guidebook comics, badges, trophies and pretty much anything else that needed art.
For several years after the convention still used my art. With absolutely no credit to me for the following years.