Problem/Motivation
Writing tests is a good approach. It helps to reduce the number of bugs as we add new features. However for patches that do not bring any new functionality but fix bugs in existing features requiring tests is a destructive policy because it slows down the process of fixing bugs in Drupal core.
It is a quite typical case, when a patch for a bug is submitted and even reviewed but then it gets declined by core committer because of lack of tests. After this the issue may get stuck for a very long time (months/years). And there is a great chance the patch will never be commited. Furthermore it also happens that a fix that was already commited is reverted because of this testing policy. Which is kind of crazy because reverting a commit that fixes a bug is like deliberately commiting this bug.
Another point here is that writing tests may require different level of skills and area of expertise than fixing a bug. Drupal testing sub-system is rather complicated. At this moment it consists of 5 (?) different types of tests. On the other hand the patches for many bugs are trivial and could be processed in novice issues.
Proposed resolution
Make writing tests for bug fixes completely optional.
For bug reports marked with "Needs tests" tag require creating a follow-up issue if the patch does not provide tests.
Remaining tasks
Discuss and get it implemented.