Note: the Opamps I have in there are LM358s, which aren't rail to rail, I would replace those with a rail to rail part in the actual device, just grabbed the first opamp in Eagle.
I usually try to avoid rail-to-rail operational amplifiers because they cost more and usually compromise performance and in the case of a power supply where extra bias supplies are easy to include, they are not really needed.
The one exception might be for high side applications where the common mode input range needs to go to the positive supply although this is usually where they have precision problems. (1) There are some non rail-to-rail input operational amplifiers which have a common mode range which extends to the positive supply like the ancient LM301A and various JFET amplifiers (TL051 series, LF351, LF355, LF356, LF357, LF441) so this can be avoided if necessary without a positive bias supply.
High power current shunts tend to limit accuracy so this might not be such a large problem. 1mA out of 1A should be barely possible but beyond that requires heroic efforts. A temperature change of 20C with a 50ppm/C shunt is 1 part in 1000.
Would the output impedance of the supply include the shunt resistor, because it's on the input of the regulator? I don't think so because the transistor inside the 3081 is basically acting as a resistor too, and we're only concerned with the resistance on the emitter to ground. The 10m ballast resistors will count for output impedance I think.
No matter where the current shunt resistor is, the difference between the error amplifier's open and closed loop gain divides it (I'm simplifying) and at high frequencies, the output impedance is determined by the output shunt capacitor. For high accuracy, the current shunt needs to be on the output (2) and if the output is an emitter follower, then the increase in impedance can actually be an advantage for stability.
What are the limitations of ground referenced current sensing? Only thing I can think of is that the negative terminal of the supply wouldn't be at ground, but it will be pretty close to it.
It moves ground away from common which is inconvenient in some designs like bipolar tracking and programmable regulators. In your example schematic, now the output voltage compared to common has an offset which depends on the current.
Dave's (and mine too now I guess) supply gets around this by having a high-side current sense, and he's got a differential/instrumentation amplifier off of the shunt. Would there still need to be a frequency compensation capacitor, maybe in parallel with the gain resistor on the AD623?
Adding a separate difference/instrumentation amplifier (3) will make compensation more difficult as I learned with my first lab power supply. I ended up needing so much compensation that the current limit performed poorly as far as speed.
I think the best overall configuration is how Tektronix did it with the PS501/PS503. Use high side current sensing on the output but instead of using a difference/instrumentation amplifier to create a ground referenced high speed current signal, do the opposite and reference the slow current control level to the high side and float the current error amplifier to follow the output.
Now the problem becomes how to do a precision level shift of a slow signal to the high side instead of a fast signal to the slow side.
If elevating the negative output from common is not a problem, then just sense the current on the low side.
For a start, I would avoid using a pre-regualtor: this adds quite some difficulties. It is only needed to get high power from the small LT3081.
Upon reconsideration, I think I will do just that. I'm not terribly concerned about efficiency and I already have the heatsinks, why buy more parts and physically isolate the RF from the rest of the board? Can't be bothered...
If the heat is not a problem, then a power transistor cascode could be added to the input of the regulator or a transistor current amplifier could be added to the regulator to bypass some of the current. But this calls into question whether an integrated regulator should be used at all.
(1) I think TI has some rail-to-rail input amplifiers where you can move the input threshold to solve this.
(2) I think some of the HP power supplies placed the current shunt on the input side of the pass transistor and then compensated for the base current error. Today a FET could be used to reduce the error.
(3) Differential amplifiers are a difference beast. I know differential, difference, and instrumentation amplifier are often used for the same thing but differential is really confusing because there are real differential amplifiers which have nothing to do with difference and instrumentation amplifiers. In the past, differential amplifiers were sometimes confusingly refereed to as push-pull amplifiers and push-pull has a completely different meaning now.