How are strikes different in any way? Strikes are when people stop working as a way to negotiate. If you're going to prevent them, then you're going to force people to work when they don't want to.
Because those people aren't saying "pay us more or we quit", they're saying "pay us more or we'll stop you from functioning". In many cases where people strike, the employer could quickly replace them if they quit (maybe not if they all quit, but they're easily replaceable individually).
How are they stopping a business from functioning? If they are sabotaging it or trespassing, that's already illegal and doesn't need to be made more illegal. If they're merely protesting, boycotting, encouraging people to go elsewhere, etc., that should remain legal as a matter of freedom of speech.
Can you fire workers on strike, and replace them? If not, that's essentially a hostage situation. They can protest and boycott all they want on their own time (after hours), but if they're paid to work, then they should work.
EDIT: What I'm trying to say is this: if the business depends on the workers, and they go on strike, and you're not allowed to fire them and hire new ones, then they're effectively "stopping a business from functioning".
"At-will" work would imply that, yes, you can fire striking workers. I can see no more reason to prohibit this than to prohibit strikes in the first place.
I don't think you even need 'at-will'. Someone that is so blatantly not doing their job that they're not even showing up to work should be trivial to fire under almost any circumstances. ahomescu1's worry is pretty unrealistic.
In most European countries, employees carrying out a legal strike are basically impossible to fire legally until the strike has ended.
But at the same time, the conditions for when a strike is legal wary substantially, and strikes for wage reasons are generally restricted to periods during wage negotiations.
