Would a ban on mobile homes in tornado-prone areas be a good idea or a bad one?

That would be a matter of individual opinion and could be debated endlessly. Generally, bans of any kind are a bad idea on the basis that they can turn normally law-abiding citizens into criminals and of course that ban has to be enforced at cost to the law-makers. In this case, the ban is in the interests of safety and can be considered a good idea on that basis. However, life would be rather boring if everything was super-safe with all risks eliminated. Carry on debating this at your leisure.

Edit:

I would like to add that most people who live in mobile homes cannot afford to buy a house. Telling them they cannot own a mobile home would leave many of them living on the street, and drive up the cost of apartments as the thousands of now homeless people tried finding a place to live.