I know there exist a plethora of reasons as to why this will never happen in the modern era or football.
However, with the Bills - Toronto Series and the obvious push on the part of Rogers / MLSE to win over the hearts and minds of the sports consumer, I really think it would be to the CFL's benefit to have one of its clubs openly challenge the NFL to a friendly contest.
Now aside from scheduling and union issues, the biggest reason why this wouldn't happen is because the NFL and those with interest in Toronto's landing an NFL team would be the only ones with something to lose.
Those with deep knowledge in football know that the economic disparities between the two leagues don't equate to disparities in talent, quality or entertainment value. The problem is that the casual sports consumer doesn't necessarily understand this. This is no more evident than in the GTA where people will go broke to see the Maple Leafs, but leave the Marlies to play in an empty arena.
I think an exhibition between a CFL and NFL team played to hybrid rules or a home & home series would break down the notion of utter supremacy that many CFL haters hold of the NFL. I'm confident the CFL club would hold their own in a hybrid match and win definitely in Canadian rules.
I enjoy football of all varieties, I just beleive the CFL is worthy of a little more respect in Southern Ontario.
I would rather everyone think of the clubs in the CFL as legitimate professional football teams, entitled to their territory and not as any less than those of the NFL.
An exhibition contest might be the way to legitimize this to everyone.