My 2 cents.

1. Count encoding includes additional information like frequency of occurance (while at the same time disregarding insubstantial differences) which, in general, is more helpful information than the index of a label as in Label encoding.

2. Count encoding can reduce the curse of dimensionality (ie learning in high-dimensional manifolds) which is known to reduce preformance, unlike Label encoding.

My 2 cents.

1. Count encoding includes additional information like frequency of occurance (while at the same time disregarding insubstantial differences) which, in general, is more helpful information than the index of a label as in Label encoding.

2. Count encoding can reduce the curse of dimensionality (ie learning in high-dimensional manifolds) which is known to reduce preformance, unlike Label encoding.

An analogy in mathematics is modulo arithmetic; It is known (in fact a theorem) that some (complex) equations do not have solutions if they do not have solutions modulo some numbers. Since modulo arithmetic is faster and easier it in fact reduces several complex problems to simpler ones, by the sole effect of combining numbers into equivalence classes (modulo operation).

Is it a panacea? Of course not, but certainly provides for easier solutions to complex problems in the cases that it holds true.