An intuition for ESC (every set is subcountable, i.e., a subquotient of the natural numbers) in a predicative framework is that everything is built up from below starting with natural numbers, so we may assume that every set can be represented as a set of codes (natural numbers) quotiented out by an equivalence relation (denoting equality of whatever the codes represent).

For the consistency of CZF + ESC (indeed, CZF + REA + ESC), see Michael Rathjen's Choice principles in constructive and classical set theories, Thm. 8.3: http://www1.maths.leeds.ac.uk/~rathjen/acend.pdf

An intuition for ESC (every set is subcountable, i.e., a subquotient of the natural numbers) in a predicative framework is that everything is built up from below starting with natural numbers, so we may assume that every set can be represented as a set of codes (natural numbers) quotiented out by an equivalence relation (denoting equality of whatever the codes represent).

For the consistency of CZF + ESC (indeed, CZF + REA + ESC), see Michael Rathjen's Choice principles in constructive and classical set theories, Thm. 8.3.