The problem is that the current noise of AZ OPs is not normal, mainly low frequency noise, but there is also a significant higher frequency background. Performance of AZ OPs depends in a more complicated way on the input impedance, than just giving a current noise number. So depending on the sensitivity of the circuit, there can be extra trouble.
Kleinstein touched the tip of the iceberg here, and after you spend some bench time testing AZ amp like '2057 and their ilk, you realize how close the datasheets come to what Mark Twain was talking about: "
There are three kinds of lies: lies, damned lies, and statistics."
The datasheets rush to show you the apparently low current input noise of these things, and then try to not really mention what's really going on with transient input current noise happening at the amp's chopper frequency, and then of course at harmonics up from there.
When you look at the input current chopper noise of a '2057 or similar - just from the datasheet - it looks like maybe you still have maybe double the input current noise of an LT1013, but still low. NOT EXACTLY! How about 100X to 600X the current noise when you look at those current spikes in detail! At first you thought you were talking about some pA or nA of current noise - but suddenly you realize you got input current spikes of some uA pounding around your sensitive circuit!
If you look at the LTC2057 datasheet, do you see how the
current input noise AT the chopper freq. isn't mentioned a lot?
So you take an LTZ1000 - which wants a QUIET QUIET QUIET and un-eventful current flow, and in return coverts that to a stable voltage across it's zener diode + transistor Vbe voltage drops - and when you slap a clock-driven, commutation switched auto-zero op amp in there an you get BLAM BLAM BLAM current spikes applied
directly to the LTZ die - especially from the inverting amp input. Those sharp, short current spikes get converted into mechanical stress waves inside the substrate crystal lattice. It's like you're hitting the LTZ die with a very small, but definite hammer effect of an AC current pulse train. These disturbances in crystal stress will start at Chopper at frequency, but by the time they reflect and modulate around the edges if the die you'll see detectable stress acoustics up into the low Mhz region.
Not to mention the other thing that happens with AZ amps: Any trace length and enclosed loop area on the amp inputs will become antennas for noise radiation of what otherwise was a very quiet, beautiful, pristine analog circuit. Especially if you have "Crop Circles" type traces or "Voodoo Slots" around the LTZ (Not complaining about TiN's board at all, but we've never seen -any- improvement with those types of design tricks - but can and does pickup and radiate noise more when traces are too long and not very efficient layout) Just when you thought you had a quiet analog board - that AZ amp inputs and power rails will be splattering ~100kHz or whatever chopper frequency hash around the area. It is a low current, but it can have enough energy to mess up nearby sensitive circuits for sure if you're not ready for it. In some cases those AZ current spikes over time can drive a crack in to the crystal substrate of whatever they are connected to - usually if there was an edge defect to begin with.
For these reasons above (and because an AZ amp offers virtually no benefit to an LTZ current driver) is why LT does NOT recommend the use of an Auto Zero type amp for an LTZ. There are other applications for an AZ amp, but this definitely is not one of them.
Remember: Plenty of workhorse 3458a's out there with ppm / yr drift rates down in the Low-PPM mud, and virtually completely stable for decades without a fuss. There are no AZ amps, slots or crop circles required. If the basic datasheet circuit is followed with a good, reasonable, efficient compact board layout - this is very hard to beat for max performance and reliability. There may be a slight thermal gradient on the non-fancy board, but if the gradient is stable (it usually is inside an enclosure) there is no effect on output. You keep air drafts away but do not OVER-insulate the LTZ board, which is just as bad as no covering at all (because the heater circuit can't servo correctly in a near 100% thermal-insulated environment). You select your heater ratio resistors for best performance in YOUR enclosure and application. After that the majority of the drift rate is dictated by the LTZ die itself, and that is beyond anyone's control after the die is singulated from the master production wafer. "It is what it is" at that point and the basic long term drift characteristics are locked in for each LTZ die at that exact moment in time it becomes separated from its siblings.
SO: In general, your Auto-Zero amp board will probably work as we're still talking fairly low current spikes input noise, but the use of Auto Zero amps with high-precision LTZ class circuits is really not recommended engineering practice - ESPECIALLY IF you are connecting a precision, sensitive die directly to the AZ amp inputs. For instance an LTZ, photodiode, zener, etc. Also you have to mitigate the chopper noise you're injecting on those op-amp power rails also, which is not insignificant either. Sometimes you realize that it's more profitable from a noise mitigation standpoint to just perform an occasional drift correction by using a conventional amp.
For the LTZ circuit especially, the '1013 is the best amp to use, and will offer maximum performance up to and including what the LTZ die is going to give you. It is tailor-made for the LTZ application.
For further reading, I suggest taking a look at
Art of Electronics Third Edition, Horowitz & Hill - look at chapter 5.10 and the section on precision op-amps. Around page 335 it gets more interesting describing most AZ amp architectures - and their test results vs datasheet noise claims.
Also take a look at page 13 here, for a good visual effect of what inputs currents are really doing on a typical AZ-type op amp - this document also describes a test procedure which we've used with some success:
https://e2e.ti.com/cfs-file/__key/telligent-evolution-components-attachments/00-14-01-00-00-70-21-03/Chopper-Noise.pdf