> Can you provide reasons?

Regrtest takes already a few minutes to run, adding these tests will make it even slower and the tradeoff might not be worthwhile (I'm assuming that most of the doctests are basic examples that are already well tested, and the occasional typos can be found by simply run `make doctest` every once in a while).
The tests currently have many failures and output, so adding them now will make the regrtest output more confusing.  Integrating this with regrtest requires some work, for example you would have to count successes/failures, add skips for certain tests and resources to control what tests should be run (there's currently a turtle going around on my screen when I run `make doctest`).  This will make regrtest even more complex.
People might not care to run these doctests if they are not touching the docs, and if they are, they might prefer to check only the specific doc file they changed.