In South Carolina the law text is broad.

It shall be unlawful for any person to drive or move or for the owner to cause or knowingly permit to be driven or moved on any highway any vehicle or combination of vehicles which is in such an unsafe condition as to endanger any person or property

Various US states have fender coverage laws:

• Fender Coverage Laws: States like California, New York, Washington, and Pennsylvania require the vehicle's fenders or mudguards to completely cover the width of the tire and wheel assembly. If a rim protrudes past the body of the car, it is a ticketable safety violation.

Ultimately, the "slab" culture that popularized swangas remains highly localized to Texas and small pockets of the American South precisely because the rest of the world has closed the legal loopholes that allow them.

I thought it was because of the difference in emissions standards

I am not a lawyer but EU Regulation No 1009/2010 on type approval requirements for wheel guards states:

2.1.1. In the part formed by radial planes at an angle of 30° towards the front and 50° towards the rear of the centre of the wheels (see Figure 1), the overall width (q) of the wheel guard shall be at least sufficient to cover the total tyre width (b) taking into account the tyre envelope as well as the extremes of the tyre/wheel combination(s) as specified by the manufacturer. In the case of twin wheels, the tyre envelopes and total width over the two tyres (t) shall be taken into account.

In short: Nothing is allowed to extend beyond the wheel guards. Now, look at the image above again.

Deviating materially from the type approval makes your car not street legal as far as I understand. But this is a matter for a lawyer. Surely there is a reason why these psychopathic car mods are impossible to find in all of the EU on public roads.