Those panhandlers are seeking that "handout," That's the purpose of panhaldling.  Some folks do pass some money out the window.  Some don't.  That's a matter of choice.  You comment addressing "encouraging" them involves finding a parking spot, going back to the individual and engaging them in a conversation.  Most motorists are going somewhere and simply don't have the time to engage with every panhandler they see.  Additionally, don't assume that every homeless and/or destitute individual wants to have a conversation with you.  

Your comparison to a stranded motorist or an injured animal is specious.  I and, I guessing, you have altered my plans, called and postponed an engagement, etc. so I could help a stranded motorist.....very different thing.

As I mentioned, if Springfield, Eugene or anyone else is truly interested in traffic safety, they should focus on enforcing those "no talking on cell phones and no texting" laws........rather than attacking panhandling.