Tests are a super helpful way to say "See, this works. Make sure it keeps working, everyone."
What about software that sends emails to people, or places orders, performs billable work, or gives people directions, or supplies them with data that they then carry forward and use in decisions or in other systems?
And are you proposing that instead of writing tests you write a play-back-able-log system that can roll back state and re-apply transformations if a given component did incorrect things?
I think sensible testing is the way forward, where sensible is appropriate to the type of application, language and requirements. 100% coverage is suitable for industrial code and 1% coverage is appropriate for toy projects. But no tests at all seems foolhardy.
You do have a point about manual testing being just as effective as automated testing, just a lot more time consuming.