We say that the Lightning Network will solve scalability issues.
Let's assume for a second that the Lightning Network is deployed to the mainnet in its final form and that hundreds of thousands of users start using it.
In this scenario, we would most likely have thousands of channels open and each user would be able to reach any other user or company with one or more hops.
How likely it would be that, at this stage, all Bitcoins will be migrated over to the Lightning Network, that channels would be kept open all the time, and that, basically, we would trade with a token issues on an alternative network (the Lightning-Bitcoin traded on the Bitcoin network)?
I suspect your assumption doesn't hold. If your point is that all bitcoins will be tied to payment channels which are to be kept open at all times, then what are you going to transfer through them anyway? I'm strongly inclined to think that it makes no sense to open the channels just for their own sake, so it should be a self-balancing system of sorts. In other words, payment channels are utilitarian in their function and no one will keep them open unless there are some coins flowing through them.