To null out charge injection spickes , sampling by adc must be in correct phase relation with chopping circuitry. Period.
ADC's Internal buffer has great advantage to synchronize all processes.
Ideally one would have the ADC sampling syncronized with the chopper amplifier. However with relatively small spikes and some filtering between the AZ amplier and the ADC (e.g. the passive RC AA filter) one can get away without this with little penalty. The spikes from integrated chopper OPs are quite short and already reduced by the limited BW of the amplifier.
Using a SD ADC chip with an AZ amplifier is nothing new or special. It is regularly done with usually little problems.
The synchronization gives a slight advantage in this respect to the ADC internal buffer. Still the buffer also has limitations, e.g. with the INL, where external buffers can be better.
External AZ OPA, even the good one like max44251 (I'd think about crappy AD8628 as a joke), configured as G=1 buffer has a few MHz bandwidth. There is no way to limit this band with G=1, so accumulated noise jump up in x1000, and excellent 5.9 nV /sqrt(Hz) becomes 6 uV-RMS, or 36 (!!!) uVp-p. Now compare to about 50 nVp-p that internal buffer has.
The noise in the full BW of the amplifier does not really matter. The SD ADC in combination with the AA filter at it's input limit the bandwidth to a low value. One may have to take care that the chopper spikes are not causing aliasing though. So the RC filter at the ADC input is important, especially with AZ amplifiers/buffer that may have extra noise in the relevant frequency range.
The point with high input impedance is for the buffer before the divider - the 2nd buffer (may be 2 for pos and neg input) is a different thing. For the input side the max44251 or OPA189 are more like a poor choice for a more conventional DMM, as they have too much current noise (e.g. 600 fA/sqrt(Hz) for the max44251) and input bias. Here one needs some compromise and the AD8628 is about at a suitable point for a normal DMM ( ~ 22 nV/sqrt(Hz) , ~ 40 fA/sqrt(Hz) and some 10 pA range input bias). The data-sheet value for the AD8628 current noise seems to be too optimistic - a common thing with AZ OP-amps. On the other side the bias specs often tend to be a bit pessimistic to cover a range of supply and CM voltages and input impedances. With care on about equal impedance one can often get a better bias current.
For the buffer after the low impedance divider one would prefer less voltage noise and current noise and bias are less relevant. Here the max44251 may be suitable but possibly overkill.
The buffers directly at the ADC may also be non AZ types, when an additional layer of switching (could also choose divider ratios) is used.