Australia has a very similar system to New Zealand, using a complex CPI based on necessities. One problem even with this is that the average wage tends to rise half as fast again. So after 20 years of 3% CPI and 4.5% wages growth, those on welfare are just as well off in survival terms as they were but everyone else is much better off. Research into satisfaction levels shows that once you reach survival level (Maslov theory), your satisfaction level relates to how well off you are in relation to those around you. Thus a millionaire feels deprived when living in a billionaire suburb.
Another way to illustrate this is to consider a welfare family living as well as a well paid worker would have in 1970 (who would have been happy with his lot). Everyone else has colour TVs and PVRs while you have a B&W TV and no modern gadgets. Not helpful of course that many of the poorer people have limited money skills.
A strange anomaly is that our politicians' pensions are indexed to AWOTE (Average Weekly Ordinary Time Earnings) that is the previously mentioned 4.5% average. Funny that.
Properly channeled this dissatisfaction is a good thing. It would give a welfare family a stronger motive to get off welfare.
Improperly channeled the anger could be utilized by the unscrupulous. Dishonest politicians, organized crime, Al Qaeda, etc come to mind.