Right now there are two places where `sys.exc_info()` calls are not required anymore:
1. https://github.com/python/cpython/blob/6e5a193816e1bdf11f5fb78d620995fd6987ccf8/Lib/doctest.py#L1352-L1353
2. https://github.com/python/cpython/blob/6e5a193816e1bdf11f5fb78d620995fd6987ccf8/Lib/doctest.py#L2640-L2641

There are also places where it is exposed as a part of public API (I am not going to change that, at least in this PR):
- https://github.com/python/cpython/blob/6e5a193816e1bdf11f5fb78d620995fd6987ccf8/Lib/doctest.py#L1757
- https://github.com/python/cpython/blob/6e5a193816e1bdf11f5fb78d620995fd6987ccf8/Lib/doctest.py#L1262

And some private APIs (out of scope as well):
- https://github.com/python/cpython/blob/6e5a193816e1bdf11f5fb78d620995fd6987ccf8/Lib/doctest.py#L244

PR is on its way!

I don't think this is worth doing in a module where we can't completely get rid of the exc_info triplet.

In other words, I don't see why it's an improvement to replace

    exception = sys.exc_info()

by 

    exception = type(exc), exc, exc.__traceback__

when sys.exc_info() does exactly what your inlined version does.

Fair enough! The only improvement is that we don't call `sys.exc_info` twice here: https://github.com/python/cpython/blob/6e5a193816e1bdf11f5fb78d620995fd6987ccf8/Lib/doctest.py#L2641-L2644

But, I think it is a minor thing.

Looks like I've misunderstood the long time goal of `sys.exc_info` refactorings. Thanks a lot for the feedback!

In the long term we will want to not have the triplet, but this is a process that will take a few python versions to complete (when 3.11 is the oldest supported version). And it is not going to be simple.

In the meantime, where there is an advantage to removing exc_info because the code would be simplified or something else is changing nearby, we can do it. But I wouldn't remove exc_info just for the sake of it - such code churn makes it hard to backport other changes.