Cleaning a Drupal database from anything which is not nodes, taxonomy and other regularities? Assuming we have an all-core Drupal site; Is there a utility or even a Drush/Dconsole command to "clean" the database of anything which is not a node, or a taxonomy or any regular core-based data of all sorts ?

In other words, a utility or command to clean from the DB anything which is, for example, a remnant of a module that we installed and then deleted that is now stuck on the DB in several places and removing it manually can be sisiphyc and or tiresome (especially when you have several cases at once).
I don't think that this is possible because the core can not know what you need before you have it configured (fields, nodetypes etc). 

You would need kind of a transaction checkpoint at the DB structure, and the possibility to rollback every structure manipulation and data therein that has happened after that point.

I usually have a system besides of my content staging system to test contributed modules. Copy content stage to dev, apply module on dev, test, rollback or move the module to content stage.

If you are the module dev yourself - make up your correct uninstalls :-)