The "new economy, old economy" idealogy doesn't work in the current model. The only way for bitcoin to get big is through the transaction between established currencies and bitcoin. By not using a limited model current currencies play the economic advantage over bitcoin in stability.
Also it couldn't be enforced and enforcement is probably a bad idea. But it would be in the best interest to exchanges and bitcoin right now to use something like forex. It can always be changed later.
A perfect model would be, banks open 7 days a week and exchanges open 7 days a week. Because banks do close, the perfect economic model doesn't apply because no money can go into exchange during the weekend but money can leave. Economics no longer apply because while the price can go down the but not up by counter buying at low prices because no new money can be put in until a certain time. And since crashes are due to the steepness of dropping prices the inability to counter buy until later increases the likelihood of significant drops leading to crashes.
Yes, bitcoin should be traded on Forex. We need the added exposure.
No, any exchange that can trade 24/7 should not limit itself except for technical reasons (2 hour downtime window for updates). If the market wants to trade, it will trade. If one exchange bars it, people will move to an exchange that will.
Don't try to regulate the market thinking that you're smarter than it. Let the market does what it does, and choose for yourself whether you want to play it or ride it.