The emitter follower has a relatively low output impedance. Typical a few ohms from the parasitic emitter resistance and than some 26 Ohm divided by the current in mA. So with a 20 K load (0.5 mA of current for the transistor) this would be a little more than 50 ohm - about comparable to the open loop output resistance of OP-amps. This is the resistance without the OP-amp for the control loop - with the feedback one would have an output restance similar to the case without the emitter follower, just without the thermal error and no output stage cross over as the output stage is class A. If there is no problem with oscillation due to excessive capacitive load the output should be able to also drive larger loads.
When driving directly a switched capacitor type ADC (most SD and SAR ADC chips) it would need extra care / filtering close to the ADC and ideally a ADC driver at the ADC. These ADCs just need a defined drive characteristic and generally don't work well with a variable impedance - the cable length alone could make a difference. So directly to the ADC is not a good input design.
Also the ADC / DAC ref. inputs may need a dedicated driver close to the chip and some want quite some capacitance there.
Chopped inputs at a DMM should include the filtering needed, so that the source impedance is not as critical. This is one difficulty in using AZ OP amps at a DMM input. If the input is sensitive to the source impedance this is more a problem with the DMM not the signal source. The HP like AZ switching produces fewer (e.g. 5-50 Hz compared to some 50 kHz) current spikes than AZ amplifiers, but the spikes tend to be larger and longer. Some settling time is usually alowed, but this may not be enough for a slow driver. The current spike from AZ switching could be an issue with the output, if build to tolerate a large capacitance, as this slow down the settling.
There is nothing bad with the LT1010. Similar to the AD8065 it may be a bit over the top. The in loop driver does not need to be low drift, low noise and low THD. One would like good speed and good tolerance to capacitive loading, whicht often comes with a bit higher power consumption. Quite some of the faster OP-amps are made with audio in mind and are thus still low noise and low THD, but this is not really needed. So the NE5532 was suggested for it's speed and availabilty, not the noise or THD. It is however quite power hungry. For a 10 V output is usually OK to power the amplifier from one the +15 ond GND, with no need to also have -15 V.