> If a homeless wanted to do some simple work (e.g. cleaning) in exchange for food and shelter would he be able to do so?

Probably, but why would you risk hiring them? The fact that they're homeless speaks to a lack of self-control. Even a perfectly healthy person who becomes homeless will get at least a bit messed up due to stress.

> Aren't there modern-day monks? Wouldn't people rather spend their life doing honest work with church than beg on the streets?

I've wondered this. We need secular monasteries, not just retreats for the wealthy. On the other hand, you can't really use your own motivations to understand why people are homeless. If they were thinking clearly and had a support network of friends / family that they weren't ashamed to reach out to, then they wouldn't be homeless.