The LT1010 has the advantage of being able to source and sink current from the output.
Sure, yet most of the (positive) linear regulators can only source current and everybody is fine with that. Could you name some common circuit(s) which requires push/pull power supply? - I'm curious. IMHO mentioned frontent of the multimeter do not require such.
I think the advantage here is that the class-ab output stage of the LT1010 performs more consistently over a wide range of output currents because it never operates in cutoff. Some high performance references use a similar output circuit and they can source and sink current as well.
The LT1010 could also be replaced with a 4 transistor complementary diamond buffer and there are some advanced low dropout complementary boosted output operational amplifier configurations which could be used also. (1) The LT1010 has the advantage of simplicity though and I suspect Linear Technology made it an understandable point in these older datasheets to show their own products like the LT1010 in application circuits even if higher performance alternatives existed.
(1) See below for an example similar to what I would try however the common emitter output configuration may not have good enough power supply rejection and requires a single operational amplifier instead of a dual or quad.