I agree with the concept, but it is hard to do when you are on the low end (and can take time to build up), and if you are on the very low end 12 months of savings for normal expenses can get wiped out with just a few minor emergencies.
Yep; that's the thing that people who didn't grow up poor miss. The 'cost' of being poor (as a percentage of income, not as an absolute figure!) is higher for poor people than the 'cost' of being well-off is for well-off people. Late fees, overdraft fees, frequent maintenance expenses stemming from owning and/or driving crap, higher interest rates, other types of pricing premiums for things stemming from their being inferior status as a buyer or a borrower of various goods and services, health, etc.
Add to that the pervasive psychological and physiological pathologies unavoidably common among poor people - whatever you think of how that reflects on their "responsibility" - and the external costs of those, and, well, you get the idea.