In exploring the image, I believe most of this comes directly from the Recommends: on postgresql-common and postgresql-NN packages (since we don't use --no-install-recommends on their installations).

When I inspect those two packages for PostgreSQL 12, the full list of Recommends: is e2fsprogs, logrotate, and sysstat, none of which appear to be important for core PostgreSQL functionality, so I think the better solution here is probably to include --no-install-recommends consistently on all our apt-get install lines to avoid these packages in the first place.

We might need to add some back manually, but that's probably a good thing too:

$ apt-get purge -s --auto-remove -o APT::AutoRemove::RecommendsImportant=false
...
The following packages will be REMOVED:
  bzip2* cron* exim4-base* exim4-config* exim4-daemon-light* file* guile-2.2-libs* krb5-locales* libevent-2.1-6* libexpat1*
  libfribidi0* libgc1c2* libgnutls-dane0* libgpm2* libgsasl7* libidn11* libkyotocabinet16v5* libltdl7* liblzo2-2* libmagic-mgc*
  libmagic1* libmailutils5* libmariadb3* libntlm0* libpopt0* libpython2.7* libpython2.7-minimal* libpython2.7-stdlib*
  libsensors-config* libsensors5* libunbound8* libwrap0* logrotate* mailutils* mailutils-common* mariadb-common* mime-support*
  mysql-common* psmisc* sysstat* xz-utils*
...

@tianon Thanks for the feedback. I've introduced --no-install-recommends where apt-get install is being made. Image size is reduced from 397MB to 314MB in the build output. That's around 80MB per image.

But I can't distinguish which of those packages (from your console output) need to be installed manually. If you can tell I can include them in the PR.

I was worried that some of these packages might be required for create extension, but I did a quick test on a couple versions of the postgis/postgis image and it works fine. Are there any other popular extensions that could be worthwhile for a quick test before merging?

Apart from that, LGTM.