A lot of people living in subsidized housing will have a stove, because Section 8 requires it from landlords. However, I know a lot of people who may be slightly above the poverty line who don't have a working stove. That included me for a while.
It would be very unusual for access to an appliance to decrease as income rises. Do you have any data to support that claim beyond your individual experience?
Did you not read what I just wrote? Section 8 housing requires these appliances. But you have to be below a certain income level to quality for Section 8 housing. It would be very reasonable to assume that once your income is above that required for Section 8 housing ($36,000 for family of 4), then if your appliance broke, it might be difficult to replace it because you don't have several thousand dollars lying around. If you've never tried to raise a family of 4 on ~$37,000, let me assure you that you will likely run into that situation sometimes.
But no, other than my personal experience, I have no data to support my claim. Just as you have none to support your counter-claim.