Secret Sharing: Is this simplification secure?
Is the above suggestion secure?
  


Sure; for any group that doesn't have a subset that's a group in $\Gamma$, they don't have enough information to reconstruct the shared secret.

Your approach is indeed a subset of Benaloh's, where you constrain the circuit to be a layer of AND gates, followed by a single OR gate.


  
  2.What's the advantage of the more general approach as presented by Stinson?
  


The size of the shares; your scheme requires a share size for an individual that is proportional to the number of groups it's a member of.  For example, if the access structure is "any of 1000 members of group A, plus any of 1000 members of group B, plus any of 1000 members of group C", then everyone's shares will be 1,000,000 times the size of the shared secret; with Benaloh's method, each share need not be any larger than the shared secret.

Of course, if the access structure is "any 500 of the 1000 member groups", you're far better off with Shamir's method, rather than either of these two...