The input stage cross over is not part of the Spice models. If at all the different noise levels may be included. The not the not so good CMRR in the cross over region and possibly different offsets on both sides are more like uncertainties with ideally 0. Similar OP models usually have zero offset.
Damn... the future is not yet today...
TI has similar technology they call e-trim.
Some part numbers: opa376, opa191, opa192.
I don't remember their specs and have no idea if they are suitable for your use, but I remember very good offset specs not far behind auto-zero chips.
The weakest part is as usual the rail-to-rail input stage. It frankly is a gimmick. 
BTW, here's the figure you are looking for from AD8605 datasheet.
As you can see, offset voltage wobble in the input crossover region can exceed 100µVpp.
(Attachment Link)
I mean TBH I'd be happy enough with 500mV to the positive rail as long as I can get everything working on 5V, that would cover almost all applications I do.
Thank you for the picture. I only found it in black and white. If I am not mistaken by the late hour, using it in an inverting configuration with a 2.5 ref voltage (what I use for pretty much everything) that would be fine. But indeed it makes less sense for non-inverting configurations.
The opa376 is indeed very interesting. The offset is pretty very low up until VCC-1.3V and it is available with the same package and pinout for 1$.
BUT after VCC-1.3V it gets in the mV range, while the AD8605 has 80uV typical with 300uV max over the whole supply range.
cons: has even worst CMRR
The TP2311 I mentioned earlier after further investigation appears to be a clone of the OPA376.
Also, the OPA2376 costs 1.2$, thus let's say it's a 60 cent opamp.
Curiously, the TP2311 chinese opamp claims much better CMRR than both
https://datasheet.lcsc.com/szlcsc/1907250931_3PEAK-TP2311-TR_C116439.pdfTo be trusted? mmh...

RRIO (Rail to Rail Input and Output)
A rail-to-rail input conflicts with precision because of crossover effects unless a boost supply is used and there are some parts which do this internally.
offset voltage under 100uV max 50uV typical
Taking advantage of low offset voltage for precision in non-inverting applications means also having a high common mode rejection ratio which the AD8605 lacks. The power supply rejection is commensurately low as well.
AD brags about low noise at 8nV/√Hz and 2.3uVpp for the AD8605 however contrasting this with a real precision part like the LT6010 (1) which is 14nV/√Hz and 0.4uVpp (!) reveals that the AD8605 has very high flicker noise which is typical of CMOS parts.
The AD8605 is not a precision operational amplifier despite its trimmed offset voltage. I would consider it more of a general purpose part and it may be completely adequate for your needs. Above I am just pointing out the more obscure issues I would consider.
- output current >40mA with 1V drop
How output current conflicts with precision because of self heating. Precision applications must minimize change in power dissipation with signal level. I would be leery of operating a part close to its maximum current rating if reliability is desired.
The cross-over region is an excellent point. I was not able to get it to act out in simulations, do you have a suggestion on how i would be able to better test this behaviour?
Doing a cross plot of the offset versus common mode voltage on an oscilloscope will reveal the problem. National Semiconductor published some application notes about it and Bob Pease discussed it.
(1) The LT6010/1/2 S/D/Q are modernized versions of the LT1008/LT1012/LT1097 S/S/S which are themselves descendants of the LM308 and LM11 but with rail-to-rail outputs and might be considered "universal" precision operational amplifiers. They are useful as a benchmark but do not really meet your other requirements.
Thank you for all this insightful information. Indeed the noise figures looked a bit misleading. [/list]