Because employers are required to pay payroll and income taxes based on where the employees are performing their work functions.

The fraud is on the employee but the tax issues fall on the employer.

The tax authorities won't see it that way.

How much due diligence are companies expected to do when it comes to these things so that if it happens anyway the employer can be considered off the hook?

Where are you going with this? It isn't really controversial at all that a business needs to pay state taxes associated with their employees resident in the state. We can speculate about some alternate tax regime that didn't have those complications but to speculate on how a business can skirt the existing requirements doesn't seem like a productive conversation

No legitimate business is going to play games trying to illegal avoid these basic state taxes. They may choose to not have employees in certain states due to particular laws though. California comes to mind...

We aren't talking about businesses not paying taxes. We are talking about employees lying about what state they are in. Which is the excuse Facebook is using to monitor employees' location via VPN and geotracking.