There was discussion a while ago that proposed a tri-state config
option: never update the remote head on fetch, always do so, or add it
only when missing:

  https://lore.kernel.org/git/20201118091219.3341585-1-felipe.contreras@gmail.com/ (local)

Thanks for linking that, I didn't think about searching for old discussion
before writing ...

I think that is a good first step, as we could stop there and leave the
default at "never" without any compatibility issues (and/or contemplate
a change in the default as a separate step).

I don't think the patch in that thread is likely to go anywhere at this
point, but if somebody wanted to pick it up, I think everybody was
positive on the general direction.

My C skills aren't great (probably an overstatement), but if Felipe or somebody
else more qualified than me doesn't want to pick this up, I'm willing to give
it a shot based on the Felipe's patch. It will take some time though :)

Thanks,
Bence