Steven, if these are not rhetorical questions and you actually do want information, here is a place to start, a summary of the results of the Jan. 2015 Eugene one night homeless count:

http://www.lanecounty.org/departments/hhs/hsc/documents/press_release_2016_pit_count.pdf

The majority of the homeless are that way temporarily, are not alcoholics, drug addicts, mentally ill or criminals -- except to the extent they're forced to be by the local camping ban. The main reason they exist is a lack of affordable housing, coupled with not enough living wage jobs.

Most are presently unsheltered because we do not have anywhere near enough shelter. Only a small percentage are publicly visible, the rest tend to hide to avoid being hassled by the cops. They are present throughout the city and nearby unincorporated areas so more rest stops will not spread them out, just provide legal controlled places for them to be. 

Your choice is between rest stops and illegal camps.