Do you think the flood of sympathy will then be unleashed, unhindered as it is by the disgusting view of the subjects of the sympathy? No, what will happen is that an issue that almost no one cares about (except, like you, in terms of it being a bother) is further removed from public view.
The chance of people being sympathetic and wanting to help those who suffer is much higher if the homeless people aren't removed from their view.