The value of tests is when the fail they show you of something you broke that you didn't realize. 80% (likely more, but I don't know how to measure) of the tests I write could safely be thrown away because they fail again - but I don't know which tests will fail and thus inform me that I broke things.

The system I'm working on has been in production for 12 years - we have added a lot of new features over those years. Many of those needed us to hook into existing code, tests help us know that we didn't break something that used to work.

Maybe that helps answer the question of why they are important to me. They might not be to your problems.