If hyper-focused on a small part of the design, an integrated zero-drift amplifier would appear to make sense, however when considering the whole design, integrated zero-drift amplifiers are not suitable for the input amplifier on a 8.5d voltmeter design (and HP agreed). Designs that use zero-drift amplifier on the input are more like "low source impedance digitiser" rather than "voltmeter" (HPM7177 being a good example where it is continuously monitoring LHC magnets in a highly stable temperature environment).
(I'm going to use the term "chopper frequency" going forward, but this could easily refer to the frequency of non-chopper zero-drift mechanisms like autozero, correlated double sampling, and higher order nested zero-drift schemes, as true chopper topology amplifiers are rarely used anymore)
1. IC AZ has no control over the charge injection spikes. With a discrete design, it's easier to have precharge phases. Furthermore, because the chopper frequency of a discrete implementation tends to be lower (1NPLC for example), it's easier to observe the charge injection spikes during development.
2. IC AZ has high input current noise. Good luck measuring high value resistors. Current noise is usually proportional to the chopper frequency. Lower frequency = lower current noise. (therefore you can see the advantage of 1NPLC vs >100kHz...)
3. So the drift of one amplifier is solved... what about the whole signal path? ADCs have 1/f noise too. Even the AD4630 which claims "1/f noise is canceled internally" on the datasheet. So now there are multiple points of the signal chain doing their own zero-drift mechanisms which is a recipe for problems. IMO it's better to do chopping on the whole signal path as one, at a frequency you control.
4. There was mention of "half the input signal gets lost" - there are topologies that avoid this, though I don't think it's a big concern for DMM inputs to have a auto-zero scheme that halves the sample rate. For a modern DMM that only has an IC ADC (no integrating ADC), I think it's sensible to have 2 distinct modes of operation - "NPLC mode" where all the auto-zero/auto-cal mechanisms are enabled, and "Digitiser mode" where they are disabled (perhaps with a single correction at the point where you change modes, and automatically thereafter at any point where the internal DMM temperature has changed 0.1 degC, with an optional user override of this behavior when you absolutely must have a contiguous stream of samples, as in the case of HPM7177).
5. Once you have a discrete zero-drift mechanism in place, other advantages come in too - that analog switch that does the switching between "Input" and "0V" can have another input to a mux that allows the selection of other voltages (like REF+), ideal for self-calibration.
6. JFET front end (whether discrete or OPA140) already has single-digit pA input bias current. Far less compensation required, if any.