Only in the effect that, and i'll use the Burton Binding Line, as a reference but it holds true in nearly every brand in the market.
If you have a board like, let's say the Burton Clash or K2 Brigade, Biax Glass, Extruded base, low-end, soft, and very easy to ride for a beginner. A binding like the Cartel with a mid-glass loaded content is likely to overpower the board. A softer flexing binding, like a Custom or a Freestyle, for that customer and that board are likely to be more appropriate as this customer, generally speaking, isn't skilled enough to compensate how they ride based on the product being less forgiving.
The Inverse is also generally true.
A mid-stiff toe to heel binding like the Cartel, is in all likelihood, more appropriate for a board like the Burton Custom or another comparable board with Triax Glass and some hits of carbon stringers, etc.
It comes down to this relationship in board material content and the relationship with the boot fit, that makes a good binding decision for most people. Which true, the board is built for some semblance of specific terrain, however, it's bill of materials and to a point shape largely dictate what binding is most appropriate.
So, in the case of "what binding is best for all mountain freestyle?" can be answered with ALL of them. From our Freestyle or our Diode are all applicable. What's the rider's ability, what board(s) are they using and what boot... these factors are they only merit in making such a decision.