You don't know what it was like in the old days. Not very good specs on op-amps. You could get something better, but they cost more and were thus less in circulation. You could get "high impedance op-amps", but they were generally merely better compared to what was common.
Hence you'd see all kinds of schemes to get better input impedance. FETs and even bipolar transistors, one to each of the inputs, and only when you really needed it.
Then CMOS and bifet opamps appeared, and worrying about input impedance pretty much went away.
yeah, I forgot that. But in my case the op amps have FET inputs so surely this means that the inputs have huge impedences?
I know in a bipolar amp that the configuration and biasing can effect the impedences but in an op amp I thought that the inputs were made to have high impedences no matter what? (no matter the configuration and close loop gain)
The opamp inputs can usually be assumed to be high impedance nodes (that is one of the definitions of an opamp). But the effect of the connected network certainly cannot. For instance, in the inverting amplifier configuration, even though the opamp inverting input does not load the circuit, the output connected back to it, does. That feedback connection forces the input node to look like a short circuit to whatever voltage is applied to the non inverting input, a condition referred to as a virtual ground.
But all the configurations on the web page you linked to are non inverting, and these generally have high impedance inputs, except for the impedance of the bias resistors connected to the input. I think these could certainly be designed to eliminate either the input follower or output follower, or to replace them with opamp versions of those followers. I think there should be at least one follower in the circuit for he total bypass case, where the downstream cable capacitance is driven by the follower, to prevent the high frequencies from being rolled off by the loading effect of that capacitance on the high source impedance.