Skin effect will follow the self inductance inside the wire, and that effect is what pushes the signal to the surface of the wire. The signal just doesn’t “go there” it is FORCED to go there as the wire center gets higher and higher impedance, or resistance, as frequency goes up. This is called wire self inductance.
A broad flat “wire” will see the same skin depth as a round wire at the same frequency EXCEPT at the edges where eddy currents cause some confusion.
True RF does not need “thick” copper shields as the thickness is unused. Spiral shields of any material or thickness makes an inductor. Bad. This is why good spiral shields to improve flex also have SHORTING folds built-in to make the shield look like a metal TUBE.
Heavy copper tape shields are used where inductively coupled energy can get onto the shield. Think cell phone tower cable and lightening as an example. Typical RF doesn’t leverage the thick copper tapes real purpose.
Proper shields have no current if they are grounded right. A shield needs to look like zero ohms resistance to the frequency you want to shield. This is called transfer impedance. We don’t want RF on our SIGNAL wire so we make that a HIGH impedance at the frequency we want to block. Where we WANT the RF to go we make it LOW impedance to say to the RF, “Hey, OVER HERE!”.
Once we get the RF onto the shield, it tries to go to ground. E=I*R so we want zero ohms times the RF to ground current to generate a small inductive coupled voltage. Both ends of the shiled need to be near the same potential to STOP current flow in the shield. If each end is the same zero resistance and with zero potential DCR difference we can’t generate a voltage as we have no resistance to drop the voltage across.
If you have terrible grounds lifting one end, called a SPG - single point ground, wall outlet ground end is best will create a current by default but MIGHT offer less noise than a true shield. This is an ANTENNA and yes, they MOVE a CURRENT from A to B by design. There is no way to get around that. It is a stop gap “easy” way to initially mitigate noise.
NEVER use a signle point ground shield unless your ground buss is BROKEN (high DCR between end points). A SPG MAKES a current to ground and inductively couples energy to the signal wires underneath by design. It just MAY be less noise than a crappy ground system in specific situations. Better is to fix your ground bus. There are strict rules on ground resistance such that shields work right.
Ethernet networks are strictly tested for RF shield performance both ingress and egress. Many feel shields are a problem when the problem is poor ground design as so many use UTP cabling that allows you to build poor ground differental networks.
Once you see how all this works, you can see the trade-offs designers have to make.