It's a trade-off between noise floor at the lower ranges, number of shunt resistors and burden voltage at the higher ranges. Apparently they optimized for the former, and not for the latter. Burden voltage tends to be worse at the top of the range. Fluke incorporates a feedback ammeter in the Fluke 8508A, but this has not (yet) trickled down to the lower models.
It is nothing to do with the noise floor. The 10mA range has a 0.03v burden voltage, and so if they could have the same for a 3A range.
They could have chosen to put an extra shunt resistor in. I don't think they were saving money, they just don't want to go there at all. As I said, the message is - if you want to measure currents of an amp or more, use a current shunt. If a circuit uses 100mA or more, you just cannot use the Agilent meter to measure the circuit's supply currents using the meter's current ranges.
Very accurate 0.01 ohm resistors can be made, and the lower the resistance, the less power dissipated so Agilent are making things very hard for themselves by using a resistor of perhaps 0.5 ohms for measuring 3 Amperes. The power dissipated by a 0.5 ohm current sense resistor is 2500 times the power in a 0.01 ohm resistor, and to meet Agilent's accuracy specs, it will cost them a lot for that shunt resistor that can stay very accurate with that amount of thermal cycling.
If they wanted to, they could add any protection that is in their cheaper hand held meters, but they just don't want to touch that. The idea of a feedback ammeter is interesting since it means there is physical shunt resistor shorting the inputs. A great idea for precision measurement - not such a great idea for measuring practical currents from a circuits power supply that may have high frequency current pulses. I can understand Agilent may not want to go that way. Fluke may drop the idea as well if customer's hate it.
I don't see the issue with protection, you just need to make sure the circuit can withstand the short circuit current at the max. rated voltage until the fuse blows. Bench meters often don't use HRC fuses and are not usually rated for high energy circuits, so I'm not sure if a large 1000V DC cap is even within specs.
I don't have the cat I 1000V and cat III 300V specs, but I think that CAT1 is tested with a 30 ohm source, cat III with a 2 ohm source.
The Agilent meter does Cat III 300V so does that mean it has to be able to handle a 150Amp fault current into the current input? That is a really big ask for a precision instrument. People often think fuses are some kind of magical protection, but they are not. By the time a fuse has completed arcing on a 300V DC fault, lots of damage can be done to a circuit. AC is much easier as it cannot arc for more than half a mains cycle. I think you would find that the main reason for the high burden voltage is the protection they have added.
But I think that it is not a matter of specs. Agilent designers will be designing beyond that, and you know that if their new meter has a higher burden voltage then their older meter, it is an intentional choice they have made. If Fluke have a lower burden voltage, then Agilent would probably argue that Fluke have got it wrong.
Fluke is saying "we will give you a lower burden voltage but be careful not to wreck the meter" and Agilent is saying "use an external current shunt for an amp or more".
Richard