I understand that OP is asking about counting bloom filters. However, a question that is equivalent in essence has already been asked and answered regarding normal bloom filters.

Why bloom filters use the same array for all k hashing algorithms

The answer above proves that using a single array (as is the case with a bloom filter or counting bloom filter) will actually result in less false positives.

That begs the question (the reverse of OP's original question), "What is the advantage of count-min sketches?"

Count-min Sketches were introduced in 2003, after counting bloom filters were already introduced, and the purpose and benefits are explained in the original paper.