Glassing does much more than simply providing cross-grain strength. It seals and waterproofs the wood and the joints between the strips. It increases the stiffness of the hull dramatically in all directions. It provides both abrasion resistance and crush resistance to the soft cedar that's typically used for stip kayaks and canoes. Without glass, you'll need to use a much tougher wood and waterproof glue in the joints (I'm assuming that you're not going to epoxy coat the wood, either). Your finish - especially on the hull - will have to be carefully maintained in order to keep water out of the wood.

The question is, are the trade-offs worth whatever benefits you perceive you'll get from not using glass?