Although we don't have the same issues as Auckland's central city with homeless people and beggars, we do have our share. I have heard of our homeless approaching female tourists on Tutantekai St in the middle of the day asking for money. These tourists reportedly looked petrified.
As a tourist town, the last thing we need is people haranguing our guests and locals for money. Granted, we don't have a homeless shelter but I believe New Zealand is very generous to its under privileged and there's a good welfare system in place which should provide enough to get by without having to beg or steal.
At least if there is a bylaw in place, a council officer can deem if the person is being a nuisance or not - and of course discretion should be used.
If we have nothing, we are powerless to act.