One additional contributor to drift in some bipolar OPAs is going to be internal input bias current compensation. The LT1001 has a bias current reduction circuit, so does the OP27 and so does its predecessor the OP07.
In most of these bias current compensation circuits there are two arms to the compensation circuit, one which measures the bias current on one side of the main differential pair (usually from a cascode bias) and one that supplies the 'make up' current to the inputs. They tend to look a awful lot like PTAT current sources.
For low drift applications it might be wise to avoid OPAs with input bias current compensation/reduction circuitry.
This is a deliberate design decision and not a factor. I doubt there is any precision operational amplifier produced which does not operate this way. The internal current biasing of the operational amplifier drives the differential input stage with a PTAT current so that the adjusted input bias current does not vary as much over temperature; it is a deliberate effort at temperature compensation. The input bias current compensation circuit just goes along for the ride.
For those who might be interested in the history of this, the improvement made to the LM301A over the LM301 was to use a PTAT current source to bias the input differential stage instead of a constant current.
I think you misunderstand precisely because you quote the LM301A, which doesn't have input bias current reduction circuitry - the bases of the input transistors have no current sources connected to them.
We're not talking about the main current source that sits in the tail of the differential pair, but something that actively reduces the input bias current (i.e. base bias), typically by mirroring the base current of a cascode transistor and injecting that into the input. This is a completely different thing to trying to even out the fall of input bias current with temperature rise by compensating out the rise in beta of the main differential pair with rising temperature by sourcing/sinking a
tail current that is PTAT, as the LM301A scheme tries to do. I believe that the OP-07 was the very first OPA to use active input bias current reduction.
There are plenty of precision OPAs that don't do active input bias reduction, the LT1013 for example.
The giveaway that you're looking at an OPA with active input bias reduction is that the input bias current on the datasheet will be (a) low for a bipolar OPA, (b) specified as +/- some current and be very close in value to the input offset current figure and (c) not a datasheet item, but they will work, albeit not at their best, without an external DC bias path to the inputs because they're already providing most of the base bias current internally. Conversely, the way to spot one without input bias current reduction is that the input
offset current and input
bias current differ by a factor of 10 or more, whereas with an active input current they are of the same order.
Again, I'm not saying that an input bias current reduction scheme is
definitely a source of offset drift, but is something to consider as a possible source of drift.