Does GFI makes equipment ground obsolete?

It provides a path to ground for fault currents

Yes. With an EGC, equipment that develops an internal ground fault (e.g. to the chassis) will trip the breaker. With a GFI only, the equipment chassis will remain hot until someone comes along and provides a path ground to trip the GFI.

Also, redundancy usually improves safety. GFIs fail alot more often than the EGC.

Cheers, Wayne

Surge protectors are certainly a lot less effective without a ground, some say not effective at all.

Appreciate the multiple purposes of that wall receptacle ground. An obvious and original purpose is to short out a circuit that would otherwise cause human electrocution. This is essential for appliances that have exposed conductive (metal) parts. GFCI (that has not been damaged by surges) also does same function.

Interconnected electronics also need (should have) a common ground connection. Again, the equipment ground accomplishes that so that voltages between appliances do rise above 30 volts and so that AC leakage has a path to bleed off to.

Two reas> If an outlet is GFI, does equipment ground still serve any useful purpose?

Because GFI's have to do something, something mechanical I think, for them to work.

The equipment ground is just a wire connected to the chassis. It's there all the time.

Also, who can be sure that one will always use any electrical device from the same outlet all the time? (unless it's a furnace or water heater, or ok, ok.... These aren't GFI outlets anyhow, iiuc.)

I'd guess a latching relay that can be put in one position electrically (tripping), but requires mechanical action (reset button) to return to the other state.