Comment by TFYS

The poor have those things because they still have some amount of power. They're still needed for work, and if you make too many of them too desperate, they can threaten the people at the top. But if you let the wealth (and power) gap get too large this will no longer be the case, and the poor might lose access to those things. If the wealth gap becomes such that the rich can afford automated production and protection but the poor can not, the current economic and political systems will no longer have a reason to give access to any of those things to the poor.