Should all search marketers be specialized in either SEO or Paid Search?

I had a talk this morning with a fellow Search Marketer.
She told me every consultant in her agency was speciliazed either in Paid Search or SEO.
The main objective behind that is to ensure each consultant is the best in his domain.
I agree with that and have to admit that, when I was managing a team of Search Marketers, I asked them to specialize for that exact purpose.

But, you still need people who are experts in both area to work on the overall search strategy.
The power of SEO & Paid Search together in a single strategy is far more efficient than tactics applied by experts in each domain.

There’s a need for specialists and all-around search marketers.