The thing to understand is that very likely your technical people are smarter than your product people. In addition, part of software development is being able to identify what needs to be solved. Any developer with a modicum of experience knows how to do this.
Just as you have a technical leader on the team, you need a technical architect on the team. That person can interface with the business or the business analyst (or both) as needed.
separate teams is a degenerate case for strong software development.
I once literally had a business person ask "who should be involved in this conversation" and my response was "product and technical so we can advise". Product responded after me with "Product" and the lack of technical there was deafening.
It becomes a power play, the theory of the different departments works out about as well as putting a racist and a black man in a room to collaborate on race relations.